7-3: Identifying Similar Triangles

1
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.

2
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.
3
Angle-Angle

• d. Compare the ratios of corresponding sides.

e. What does this tell us about the triangles?
4
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.

5
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.
6
Side-Side-Side

• c. Compare corresponding angles.

d. What is true about the triangles?
7
Side-Side-Side Triangle Similarity Theorem

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

8
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.
9
Side-Angle-Side

• c. What is true about the triangles?

10
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.

11
Equality Properties of Similarity

• Similarity of figures is reflexive, symmetric and
  transitive.

12
Reflexive Property of Similarity

• F F

13
Symmetric Property of Similarity

• If F G, then G F.

14
Transitive Property of Similarity

• If F G and G H, then F H.

15
Are the following triangles similar? Justify your
response.
7.2
12
12
20
9
15
16
Are the triangles below similar? Justify with a
postulate or theorem.
17
If AB // EF, AD 9, DB 16, EC 2(AE),
determine AE, AC, BC and EF
C
H
E
F
A
B
D
18
Use similar triangles to answer the question
below.

• At 400 a yard stick cast a 5 foot shadow. How
  tall is a tree that has an 18 foot shadow at the
  same time?

19

• 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?
• 10
• 20
• 25
• 30
• 35

B
D
10
C
6
18
A
E
20
Solve for x.
21
Given LP // MN
L
P
J
M
N
22
(No Transcript)
23
Assignment

• pages 358 361,
• 13-23 (odds), 27, 37, 39-47 (all).