geometry lesson 7 – 3 similar triangles objective: identify similar triangles using the aa...

GeometryLesson 7 – 3

Similar Triangles

Objective:Identify similar triangles using the AA Similarity postulate and the

SSS and SAS Similarity Theorem.Use similar triangles to solve problems.

Similar TrianglesAngle-Angle (AA) Similarity If two angles of one triangle are congruent to two

angles of another triangle, then the triangles are similar.

Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.

75 48

JKL ~ QPM By AA similarity.

.intaltWR .intaltTX

SRX ~ SWT By AA similarity

Determine whether the triangles are similar. If so, write a similarity statement. Explain your

reasoning.

46 43

No triangles are notsimilar since thereare no 2 angles the same.

JKL ~ PQLLPQLJK

LL

By AA similarity

TheoremSide-Side-Side (SSS) Similarity If the corresponding side lengths of two

triangles are proportional, then the triangles are similar.

TheoremSide-Angle-Side (SAS) Similarity If the lengths of two sides of one triangle

are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.

Determine whether the triangles are similar. If so, write a similarity statement.

Explain.

9.12

5

20

8

15

6

0.4 = 0.40.4 = 0.40.4 = 0.4

PQR ~ STR

By SSS similarity

Determine whether the triangles are similar. If so, write a similarity statement.

Explain.

12

16

9

12

6

8

A. Uses SAS similarity

C. Uses AA similarityD. Uses SSS similarity

B. Does not have a congruent included angle. No similarity

B is the only choice that satisfies a similarity condition. SSS similarity.

Determine whether the triangles are similar. If so, write a similarity statement.

Explain.

15

10

12

8

AA

AEF ~ ACB

By SAS Similarity

Find BE and AD

5.35

3 x

10.5 = 5x2.1 = x

35

3

y

y

3y + 9 = 5y9 = 2y

BE = 2.1AD = 4.5 + 3 = 7.5

Whole sideof one triangleto whole side of other triangle.

4.5 = y

Find QP and MP

53

36

6

5

5

x

48 = 30 + 6x18 = 6x3 = x

QP = 3MP = 5 + 3 = 8

QP = 3MP = 8

Find WR and RT

10

8

62

6

x

x

10x + 60 = 16x + 4812 = 6x2 = x

WR = x + 6 = 8

RT = 2x + 6 = 10

Real worldAdam is standing next to the Palmetto Building in Columbia, South Carolina. He is 6 feet tall and the length of his shadow is 9 feet. If the length of the shadow of the building is 322.5 feet, how tall is the building?

5.3229

6 x

9x = 1935x = 215

The Palmetto building is 215 feet tall.

Homework

Pg. 479 1 – 8 all, 10 – 24 E, 38, 42 – 56 E