[G] Geometry

Students’ prior knowledge includes:

• Students understand congruence and similarity using physical models, transparencies, or geometry software (grade 8)
• Students understand and apply the Pythagorean Theorem (grade 8)
• Student solve real-world and mathematical problems involving volume of cylinders, cones and spheres (grade 8)
• Students draw, construct and describe geometrical figures and describe the relationships between them (grade 7)
• Students solve real-life and mathematical problems involving angle measures, area, surface area, and volume (grade 7)
Congruence
• Experiment with transformations in the plane.
• Understand congruence in terms of rigid motions.
• Prove and apply geometric theorems.
• Make geometric constructions.
Similarity, Right Triangles, and Trigonometry
• Understand similarity.
• Prove theorems involving similarity.
• Define trigonometric ratios and solve problems involving right triangles.
• Apply trigonometry to general triangles.
Circles
• Understand and apply theorems involving circles.
• Find arc lengths and areas of sectors of circles.
Expressing Geometric Properties with Equations
• Understand and use conic sections.
• Use coordinates to verify simple geometric theorems algebraically
Geometric Measurement and Dimension
• Explain surface area and volume formulas and use them to solve problems.
• Visualize relationships between two-dimensional and three-dimensional objects.
Modeling with Geometry
• Apply geometric concepts in modeling situations

MAT-HS.G [G] Overview: Geometry

MAT-HS.G-SRT Domain: [G-SRT] Similarity, Right Triangles, and Trigonometry

• MAT-HS.G-SRT.01 Verify experimentally the properties of dilations
• G-SRT.01.a A line not passing through the center to a parallel line, center line unchanged
• G-SRT.01.b A line segment is longer or shorter in the ratio given by the scale factor
• MAT-HS.G-SRT.02 Use definition of similarity/transformations to see if 2 figures are similar
• MAT-HS.G-SRT.03 Use similarity transformations to establish the AA criterion for two triangles
• MAT-HS.G-SRT.04 Prove theorems about triangles
• MAT-HS.G-SRT.05 Use congruence/similarity criteria to solve problems and to prove relationships
• MAT-HS.G-SRT.06 Understand that side ratios in right triangles are properties of the angles
• MAT-HS.G-SRT.07 Explain the relationship between the sine and cosine of complementary angles
• MAT-HS.G-SRT.08 Apply trigonometric ratios and the Pythagorean Theorem to solve right triangles
• MAT-HS.G-SRT.08.a Apply trigonometric ratios and the Pythagorean Theorem to solve right triangles
• MAT-HS.G-SRT.08.b Apply trigonometric ratios and the Pythagorean Theorem to solve special triangles
• MAT-HS.G-SRT.09 Derive the formula A = 1/2 ab sin( C ) for the area of a triangle
• MAT-HS.G-SRT.10 Prove the Laws of Sines and Cosines and use them to solve problems
• MAT-HS.G-SRT.11 Apply the Law of Sines and the Law of Cosines to find unknown measurements

MAT-HS.G-C Domain: [G-C] Circles

• MAT-HS.G-C.01 Prove all circles are similar
• MAT-HS.G-C.02 Identify and describe relationships among inscribed angles, radii, and chords
• MAT-HS.G-C.03 Construct the inscribed and circumscribed circles of a triangle
• MAT-HS.G-C.04 Construct a tangent line from a point outside a given circle to the circle
• MAT-HS.G-C.05 Show the length of the arc intercepted by an angle proportional to the radius

MAT-HS.G-GPE Domain: [G-GPE] Expressing Geometric Properties with Equations

• MAT-HS.G-GPE.01 Use Pythagorean Theorem to derive the equation of a circle
• MAT-HS.G-GPE.02 Derive the equation of a parabola given a focus and directrix
• MAT-HS.G-GPE.03 Derive the equations of ellipses and hyperbolas given foci, using the fact
• MAT-HS.G-GPE.04 Use coordinates to prove simple geometric theorems algebraically
• MAT-HS.G-GPE.05 Prove the slope criteria for parallel and perpendicular lines
• MAT-HS.G-GPE.06 Find the point on a line between two points that partitions it in a given ratio
• MAT-HS.G-GPE.07 Use coordinates to compute perimeter of polygons, area of triangles/rectangles

MAT-HS.G-GMD Domain: [G-GMD] Geometric Measurement and Dimension

• MAT-HS.G-GMD.01 Support formulas for circumference/area(circle) & volume(cylinder/pyramid/cone)
• MAT-HS.G-GMD.02 Give an informal argument using Cavalieri's principle for the formulas for
• MAT-HS.G-GMD.03 Use volume formulas for cylinders, pyramids, cones, and spheres
• MAT-HS.G-GMD.04 Identify the shapes of 2D cross-sections of 3D objects

MAT-HS.G-MG Domain: [G-MG] Modeling with Geometry

• MAT-HS.G-MG.01 Use geometric shapes, measures, and properties to describe objects
• MAT-HS.G-MG.02 Apply concepts of density based on area and volume in modeling situations
• MAT-HS.G-MG.03 Apply geometric methods to solve design problems

A Sample of HS Math Concept Geometry to Become Ready for College and Career

Congruence

• Experiment with transformations in the plane.
• Understand congruence in terms of rigid motions.
• Prove and apply geometric theorems.
• Make geometric constructions

Similarity, Right Triangles, and Trigonometry

• Understand similarity.
• Prove theorems involving similarity.
• Define trigonometric ratios and solve problems involving right triangles.
• Apply trigonometry to general triangles.

Circles

• Understand and apply theorems involving circles.
• Find arc lengths and areas of sectors of circles.

Expressing Geometric Properties with Equations

• Understand and use conic sections.
• Use coordinates to verify simple geometric theorems algebraically.

Geometric Measurement and Dimension

• Explain surface area and volume formulas and use them to solve problems.
• Visualize relationships between two-dimensional and three-dimensional objects.

Modeling with Geometry

• Apply geometric concepts in modeling situations