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True or False???If False, give a counterexample.
Two triangles are always similar.
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True or False???If False, give a counterexample.
Two isosceles triangles are always similar.
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Two equilateral triangles are always similar.
True or False???If False, give a counterexample.
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True or False???If False, give a counterexample.
Two rectangles are always similar.
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Two squares are always similar.
True or False???If False, give a counterexample.
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True or False???If False, give a counterexample.
Two trapezoids are always similar.
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Two isosceles trapezoids are always similar.
True or False???If False, give a counterexample.
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True or False???If False, give a counterexample.
Two regular pentagons are always similar.
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Two circles are always similar.
True or False???If False, give a counterexample.
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HW Solutions p. 499500
# 226 even, 32, 36
2. False
4. True
6. False
8. True
10. True
12. 1/1000 = .001
14. QRST ~ XWZY; 3/4
16. ABCD ~ FGHE; 4/5
18. ABC ~ FED; 7/5
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20. 32
22. 6 7/8 = 6.875
24. 14
26. -10 or 10
32. x = 16
y = 4.5
z = 7.5
34. 0.029 ft.
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Chapter 10 Similarity
102 Proving Triangles Similar
Objective: Use postulates and theorems to provetriangles similar.
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Definition of Similar Figures
all corresponding angles are congruent
all corresponding sides are proportional
Recall:
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3 shortcuts to show two triangles are similar
Postulate 101 (AA ~ Post)
AngleAngle Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
T
R S
P
LM
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Theorem 101 (SAS ~ Thm)
SideAngleSide Similarity Theorem
If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar.
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Theorem 102 (SSS ~ Thm)
SideSideSide Similarity Theorem
If the corresponding sides of two triangles are proportional, then the triangles are similar.
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Are these triangles similar? Why?
R
WS
V
B
45° 45°6
6
9 8 8
12
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HW # 113
p. 507508 # 112, skip #10
