Applied Geometry

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Transcript Applied Geometry

Geometry
Lesson 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 Triangles
Angle-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.
R  W alt int .
X  T alt int .
 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 not
similar since there
are no 2 angles the
same.
L  L
LJK  LPQ
 JKL ~  PQL
By AA similarity
Theorem
Side-Side-Side (SSS) Similarity

If the corresponding side lengths of two
triangles are proportional, then the
triangles are similar.
Theorem
Side-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.
6
8
5


15 20 12.9
0.4 = 0.4
0.4 = 0.4
0.4 = 0.4
PQR ~ STR
By SSS similarity
Determine whether the triangles are
similar. If so, write a similarity
statement. Explain.
8 12 16


6 9 12
A. Uses SAS similarity
C. Uses AA similarity
D. 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.
8 10

12 15
A  A
AEF ~ ACB
By SAS Similarity
Find BE and AD
3
x

5 3.5
Whole side
of one triangle
to whole side
of other triangle.
10.5 = 5x
2.1 = x
3
y

5 y3
3y + 9 = 5y
9 = 2y
4.5 = y
BE = 2.1
AD = 4.5 + 3 = 7.5
Find QP and MP
5
6

5 x 633
5
48 = 30 + 6x
18 = 6x
3=x
QP = 3
MP = 5 + 3 = 8
QP = 3
MP = 8
Find WR and RT
x6
8

2 x  6 10
10x + 60 = 16x + 48
12 = 6x
2=x
WR = x + 6 = 8
RT = 2x + 6 = 10
Real world
Adam 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?
6
x

9 322.5
9x = 1935
x = 215
The Palmetto building is
215 feet tall.
Homework
Pg. 479 1 – 8 all, 10 – 24 E, 38,
42 – 56 E