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- Common Core MathK - 8High School

# Geometry: Similarity, Right Triangles, and Trigonometry

619 questions32 skills

# Geometry: Similarity, Right Triangles, and Trigonometry

619 questions32 skills

## HSG-SRT.A.1

66 questions4 skills

Verify experimentally the properties of dilations given by a center and a scale factor:

## HSG-SRT.A.1a

24 questions1 skill

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.

## HSG-SRT.A.1b

30 questions2 skills

The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

## HSG-SRT.A.2

26 questions2 skills

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.

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Skills for this standard are coming soon.

## HSG-SRT.B.4

15 questions1 skill

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.**HSG-SRT.B.5*

*312 questions16 skills*

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Determine congruent triangles

Find angles in congruent triangles

Solve triangles: angle bisector theorem

Determine similar triangles: Angles

Special right triangles

Determine similar triangles: SSS

Solve similar triangles (basic)

Solve similar triangles (advanced)

Use similar triangles

Prove triangle similarity

Justify constructions

Use ratios in right triangles

Find angles in isosceles triangles

Prove triangle properties

Prove parallelogram properties

Prove triangle congruence

## HSG-SRT.C.6

30 questions2 skills

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.

## HSG-SRT.C.7

16 questions1 skill

Explain and use the relationship between the sine and cosine of complementary angles.

## HSG-SRT.C.8

116 questions6 skills

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Derive the formula

*A*= 1/2*ab*sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. Skills for this standard are coming soon.

## HSG-SRT.D.10

74 questions3 skills

Prove the Laws of Sines and Cosines and use them to solve problems.

## HSG-SRT.D.11

74 questions3 skills

Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.