7-3: Identifying Similar Triangles

7-3: Identifying Similar Triangles

Expectations:G2.3.2: Use theorems about congruent

triangles to prove additional theorems and solve problems.

G2.3.3: Prove that triangles are similar by SSS, SAS and AA conditions for similarity.

04/20/23 7-3 Similar Triangles

Angle-Angle a. Draw two triangles with angle

measures of 75° and 65°.

b. Label the 75° angles ∠A and ∠X.

c. Label the 65° angles ∠B and ∠Y.

04/20/23 7-3 Similar Triangles

Angle-Angle d. Compare the ratios of corresponding sides.

e. What does this tell us about the triangles?

04/20/23 7-3 Similar Triangles

Angle-Angle Triangle Similarity Theorem

If two angles of a first triangle are congruent to two angles of a second triangle, then the triangles are similar.

04/20/23 7-3 Similar Triangles

Side-Side-Side a. Draw ∆ABC such that AB = 4,

BC = 6 and AC = 7.b. Draw ∆DEF such that DE = 8,

EF = 12 and DF = 14.

04/20/23 7-3 Similar Triangles

Side-Side-Side c. Compare corresponding angles.

d. What is true about the triangles?

04/20/23 7-3 Similar Triangles

Side-Side-Side Triangle Similarity Theorem

If the measures of the corresponding sides of 2 triangles are proportional, then the triangles are similar.

04/20/23 7-3 Similar Triangles

Side-Angle-Side a. Draw ∆KLM such that KL = 4,

LM = 5 and m∠L = 60°.

b. Draw ∆RST such that RS = 8, ST = 10 and m∠S = 60°.

04/20/23 7-3 Similar Triangles

Side-Angle-Side c. What is true about the triangles?

04/20/23 7-3 Similar Triangles

Sid-Angle-Side Triangle Similarity Theorem

If the measures of two sides of one triangle are proportional to two sides of a second triangle and the included angles are congruent, then the triangles are similar.

04/20/23 7-3 Similar Triangles

Equality Properties of Similarity

Similarity of figures is reflexive, symmetric and transitive.

04/20/23 7-3 Similar Triangles

Reflexive Property of Similarity

F ~ F

04/20/23 7-3 Similar Triangles

Symmetric Property of Similarity

If F ~ G, then G ~ F.

04/20/23 7-3 Similar Triangles

Transitive Property of Similarity

If F ~ G and G ~ H, then F ~ H.

04/20/23 7-3 Similar Triangles

Are the following triangles similar? Justify your response.

20 12

15

7.212

9

04/20/23 7-3 Similar Triangles

Are the triangles below similar? Justify with a postulate or

theorem.

04/20/23 7-3 Similar Triangles

If AB // EF, AD = 9, DB = 16, EC = 2(AE), determine AE, AC, BC and

EF

A D B

FHE

C

04/20/23 7-3 Similar Triangles

Use similar triangles to answer the question below.

At 4:00 a yard stick cast a 5 foot shadow. How tall is a tree that has an 18 foot shadow at the same time?

04/20/23 7-3 Similar Triangles

In the figure below, segment AB ⊥ segment DE. The measure of ∠CAD is equal to the measure of ∠CEB. The length of segment CA is 6 units and the length of segment CE is 187 units. If the length of segment AD is 10 units, what is the length of segment EB?

A.10B.20C.25D.30E. 35

04/20/23 7-3 Similar Triangles

A

10

D

C

18

E

B

6

Solve for x.

04/20/23 7-3 Similar Triangles

Given: LP // MN

Prove: LJ PJ

LN JM

PL

M N

J

04/20/23 7-3 Similar Triangles

04/20/23 7-3 Similar Triangles

Assignmentpages 358 – 361, # 13-23 (odds), 27, 37, 39-47 (all).

04/20/23 7-3 Similar Triangles