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Math

Indiana Math

Geometry: Triangles

G.T.1

Prove and apply theorems about triangles, including:

G.T.1.a

Interior angles of a triangle sum to 180°

G.T.1.b

The Isosceles Triangle Theorem and its converse
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G.T.1.c

The Pythagorean Theorem

G.T.1.d

The segment joining midpoints of two sides of a triangle is parallel to the third side and half the length
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G.T.1.e

A line parallel to one side of a triangle divides the other two proportionally, and its converse
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G.T.1.f

The Angle Bisector Theorem
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G.T.1.g

Triangle inequality
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G.T.1.h

Inequality in one triangle
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G.T.1.i

Hinge Theorem and its converse (E)
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G.T.2

Fully covered
Prove and apply criteria for triangle congruence (ASA, SAS, AAS, SSS, and HL) from the definition of congruence in terms of rigid motions. (E)

G.T.3

Fully covered
Use the definition of similarity in terms of similarity transformations to determine if two given triangles are similar. Explore and develop the meaning of similarity for triangles.

G.T.4

Fully covered
Use congruent and similar triangles to solve real-world and mathematical problems involving sides, perimeters, and areas of triangles. (E)

G.T.5

Mostly covered
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.

G.T.6

Mostly covered
Use trigonometric ratios (sine, cosine, tangent, and their inverses) and the Pythagorean Theorem to solve real-world and mathematical problems involving right triangles. (E)

G.T.7

Not covered
Use the relationship between the sides of special right triangles (30° - 60° and 45° - 45°) to solve real-world and other mathematical problems. (E)
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