Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA...
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Transcript of Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA...
![Page 1: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/1.jpg)
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.
![Page 2: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/2.jpg)
Similar TrianglesAngle-Angle (AA) Similarity If two angles of one triangle are congruent to two
angles of another triangle, then the triangles are similar.
![Page 3: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/3.jpg)
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
![Page 4: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/4.jpg)
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
![Page 5: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/5.jpg)
TheoremSide-Side-Side (SSS) Similarity If the corresponding side lengths of two
triangles are proportional, then the triangles are similar.
![Page 6: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/6.jpg)
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.
![Page 7: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/7.jpg)
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
![Page 8: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/8.jpg)
Determine whether the triangles are similar. If so, write a similarity statement.
Explain.
12
16
9
12
6
8
![Page 9: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/9.jpg)
A. Uses SAS similarity
C. Uses AA similarityD. Uses SSS similarity
B. Does not have a congruent included angle. No similarity
![Page 10: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/10.jpg)
B is the only choice that satisfies a similarity condition. SSS similarity.
![Page 11: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/11.jpg)
Determine whether the triangles are similar. If so, write a similarity statement.
Explain.
15
10
12
8
AA
AEF ~ ACB
By SAS Similarity
![Page 12: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/12.jpg)
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
![Page 13: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/13.jpg)
Find QP and MP
53
36
6
5
5
x
48 = 30 + 6x18 = 6x3 = x
QP = 3MP = 5 + 3 = 8
QP = 3MP = 8
![Page 14: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/14.jpg)
Find WR and RT
10
8
62
6
x
x
10x + 60 = 16x + 4812 = 6x2 = x
WR = x + 6 = 8
RT = 2x + 6 = 10
![Page 15: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/15.jpg)
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.
![Page 16: Geometry Lesson 7 – 3 Similar Triangles Objective: Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorem.](https://reader033.fdocuments.net/reader033/viewer/2022061413/5697bfc31a28abf838ca5644/html5/thumbnails/16.jpg)
Homework
Pg. 479 1 – 8 all, 10 – 24 E, 38, 42 – 56 E