MAT-HS.G-SRT.01
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MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Understand similarity in terms of similarity transformations
MAT-HS.G-SRT.01 Verify experimentally the properties of dilations given by a center and a scale factor.
- a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
- b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can verify experimentally the properties of dilations given by a center and a scale factor.
- I can verify experimentally that a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
- I can verify experimentally, that when performing dilations of a line segment, the image segment becomes longer or shorter based on the ratio given by the scale factor.
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
- |
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. |
- |
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). |
- |
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
- |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
- |
Resources
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MAT-HS.G-SRT.02
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MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Understand similarity in terms of similarity transformations
MAT-HS.G-SRT.02 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
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Student Learning Targets:
Knowledge Targets
- I can develop the definition of similarity using the idea of dilation transformations.
Reasoning Targets
- I can determine congruence and similarity among geometric objects.
- I can use similarity or congruence to solve for a missing side/angle.
- I can determine whether two figures are similar.
- I can explain similarity based on the equality of corresponding angles and the proportionality of corresponding sides.
Skills (Performance) Targets
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
- |
| |
3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. |
- |
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). |
- |
| |
1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
- |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
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Resources
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MAT-HS.G-SRT.03
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MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Understand similarity in terms of similarity transformations
MAT-HS.G-SRT.03 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can use the properties of similarity transformations to prove triangles are similar by AA criterion.
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
- |
| |
3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. |
- |
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). |
- |
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
- |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
- |
Resources
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MAT-HS.G-SRT.04
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MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Prove theorems involving similarity
MAT-HS.G-SRT.04 Prove theorems about triangles.
Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. |
Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can use AAA, SAS, SSS similarity theorems to prove triangles are similar.
- I can use triangle similarity to prove other theorems about triangles.
- I can prove a line parallel to one side of a triangle divides the other two proportionally, and it’s converse.
- I can prove the Pythagorean Theorem using triangle similarity.
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
- |
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. |
- |
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). |
- |
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
- |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
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Resources
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MAT-HS.G-SRT.05
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MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Prove theorems involving similarity
MAT-HS.G-SRT.05 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
- I can determine congruence and similarity among geometric objects.
- I can use similarity or congruence to solve for a missing side/angle.
Skills (Performance) Targets
- I can use similarity and congruence criteria to solve real world problems.
- I can use congruence and similarity to prove relationships involving geometric figures.
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
- |
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. |
- |
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). |
- |
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
- |
| |
0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
- |
Resources
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MAT-HS.G-SRT.05.a |
MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Prove theorems involving similarity
MAT-HS.G-SRT.05.a Use congruence to solve problems in geometric figures.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| Advanced |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations.
- Error analysis (explain why the reasoning of others is incorrect)
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Explain why the answer is incorrect and give the correct answer.
 
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| Proficient |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations.
- Use congruence to solve problems.
- Use congruence to show relationships in geometric figures (using CPCTC)
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Two door stops have cross sections that are right triangles. They both have a 200 angle and the length of the side between the 900 and the 200 angles are equal. Are the cross sections congruent? Explain.
Solve for x and y:
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| Progressing |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content).
- recognizes the congruence criteria for triangles (SAS, ASA, etc.)
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recognize and use specific terminology such as:
Corresponding angles, corresponding sides, congruence statement
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Identity all the pairs of corresponding sides and angles. Then write a congruence statement.
 
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| Beginning |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
- |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
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Resources
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MAT-HS.G-SRT.05.b |
MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Prove theorems involving similarity
MAT-HS.G-SRT.05.b Use similarity criteria to solve problems in geometric figures.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| Advanced |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations.
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| Proficient |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations.
- use similarity properties and proportions to solve for missing measurements
- use similarity to prove relationships in geometric figures
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Find the height of the tree.
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| Progressing |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content).
- can solve provided proportionality problems
- can recognize vocabulary such as congruence, similarity, scale factor, ratio and proportion
- recognizes the similarity criteria for triangles (SAS, SSS, AA)
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Identify if the given triangles are similar. If they are similar, give the scale factor.
Solve for x.
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| Beginning |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
- |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
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Resources
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MAT-HS.G-SRT.05.c |
MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Prove theorems involving similarity
MAT-HS.G-SRT.05.c Use similarity criteria to prove relationships in geometric figures.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| Advanced |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| Proficient |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations.
- Use AA, SSS, and SAS Similarity Theorems to prove triangles similar
- Justify conclusions using valid mathematical arguments.
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Sketch the triangles using the given description. Explain/Justify whether the two triangles can be similar.
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| Progressing |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content).
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recognize vocabulary such as similarity, corresponding sides, and proportional
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recognizes the similarity criteria for triangles (SAS, AA, SSS)
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Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| Beginning |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
- |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
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Resources
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MAT-HS.G-SRT.06
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MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Define trigonometric ratios and solve problems involving right triangles.
MAT-HS.G-SRT.06 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
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Student Learning Targets:
Knowledge Targets
- I can show that the side ratios are the same in similar right triangles, which leads to the definition of trigonometric ratios for acute angles.
Reasoning Targets
Skills (Performance) Targets
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
- |
| |
3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. |
- |
| |
2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). |
- |
| |
1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
- |
| |
0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
- |
Resources
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MAT-HS.G-SRT.07
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MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Define trigonometric ratios and solve problems involving right triangles.
MAT-HS.G-SRT.07 Explain and use the relationship between the sine and cosine of complementary angles.
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Student Learning Targets:
Knowledge Targets
- I can show that the side ratios are the same in similar right triangles, which leads to the definition of trigonometric ratios for acute angles.
Reasoning Targets
- I can explain the relationship between the sine and cosine of complementary angles.
Skills (Performance) Targets
- I can use the relationship between the sine and cosine of complementary angles.
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
- |
| |
3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. |
- |
| |
2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). |
- |
| |
1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
- |
| |
0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
- |
Resources
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