MAT-10 Standards
Completion requirements
ALL
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MAT-10.GM.09
MAT-10.GM.09 Prove and apply theorems about lines and angles.Progressions
Angles/Triangles
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MAT-10.GM.10
MAT-10.GM.10 Prove and apply theorems about triangles.Progressions
Two-Dimensional Shapes
Angles/Triangles
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MAT-10.GM.11
MAT-10.GM.11 Prove and apply theorems about parallelograms.Progressions
Two-Dimensional Shapes
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MAT-10.GM.12
MAT-10.GM.12 Make basic geometric constructions (e.g., segment, angle, bisectors, parallel and perpendicular lines) with a variety of tools and methods.Progressions
Compose Shapes
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MAT-10.GM.13
MAT-10.GM.13 Apply basic constructions to create polygons such as equilateral triangles, squares, and regular hexagons inscribed in circles.Progressions
Compose Shapes
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MAT-10.GM.14
MAT-10.GM.14 Verify experimentally and justify the properties of dilations given by a center and a scale factor.Progressions
Unit Size and Scale
Transformations
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MAT-10.GM.15
MAT-10.GM.15 Use transformations to decide if two given figures are similar. Apply the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.Progressions
Ratio and Proportional Relationships
Transformations
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MAT-10.GM.16
MAT-10.GM.16 Prove similarity theorems about triangles.Progressions
Ratio and Proportional Relationships
Transformations
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MAT-10.GM.17
MAT-10.GM.17 Apply knowledge of congruence and similarity criteria for triangles to solve problems and to prove relationships in various geometric figures.Progressions
Transformations
Congruence and Similarity
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MAT-10.GM.18
MAT-10.GM.18 Recognize how the properties of similar right triangles allow the trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.Progressions
Ratio and Proportional Relationships
Angles/Triangles
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MAT-10.GM.19
MAT-10.GM.19 Explain and use the relationship between the sine and cosine of complementary angles.Progressions
Angles/Triangles
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MAT-10.GM.20
MAT-10.GM.20 Solve applied problems involving right triangles using trigonometric ratios, the Pythagorean Theorem, and special right triangles (30°-60°-90° and 45°-45°-90°).Progressions
Ratio and Proportional Relationships
Angles/Triangles
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MAT-10.GM.21
MAT-10.GM.21 Solve unknown sides and angles of non-right triangles using the Laws of Sines and Cosines.Progressions
Not listed
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MAT-10.GM.22
MAT-10.GM.22 Apply theorems about relationships between line segments and circles or angles and circles formed by radii, diameter, secants, tangents,and chords to find unknown lengths or angles.Progressions
Circle Measurements
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MAT-10.GM.23
MAT-10.GM.23 Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.Progressions
Angles/Triangles
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MAT-10.GM.24
MAT-10.GM.24 Construct a tangent line from a point outside a given circle to the circle.Progressions
Angles/Triangles
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MAT-10.GM.25
MAT-10.GM.25 Explain and use the formulas for arc length and area of sectors of circles.Progressions
Ratio and Proportional Relationships
Measure Length
Circle Measurements
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MAT-10.GM.26
MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.Progressions
Unit Size and Scale
Measure Length
Angles/Triangles
Circle Measurements
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MAT-10.GM.27
MAT-10.GM.27 Develop and verify the slope criteria for parallel and perpendicular lines. Apply the slope criteria for parallel and perpendicular lines to solve problems.Progressions
Coordinate Plane
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