Area

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Similar Triangles 8.3
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• Identify similar triangles.

• Learn the definition of AA, SAS, SSS similarity.

• Use similar triangles to solve problems.

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Explain why the triangles are similar and write a
similarity statement.
?BCA ? ?ECD by the Vertical Angles Theorem.
Also, ?A ? ?D by the Right Angle Congruence
Theorem.
Therefore ?ABC ?DEC by AA Similarity.
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Explain why the triangles are similar and write a
similarity statement.
?D ? ?H by the Definition of Congruent Angles.
Arrange the sides by length so they correspond.
Therefore ?DEF ?HJK by SAS Similarity.
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Explain why the triangles are similar and write a
similarity statement.
Arrange the sides by length so they correspond.
Therefore ?PQR ?STU by SSS similarity.
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Explain why the triangles are similar and write a
similarity statement.
?TXU ? ?VXW by the Vertical Angles Theorem.
Arrange the sides by length so they correspond.
Therefore ?TXU ?VXW by SAS similarity.
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Explain why the triangles are similar and write
a similarity statement.
By the Triangle Sum Theorem, m?C 47, so ?C ?
?F. ?B ? ?E by the Right Angle Congruence
Theorem. Therefore, ?ABC ?DEF by AA Similarity.
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Determine if the triangles are similar, if so
write a similarity statement.
By the Definition of Isosceles, ?A ? ?C and ?P ?
?R. By the Triangle Sum Theorem, m?B 40, m?C
70, m?P 70, and m?R 70.
Therefore, ?ABC ?DEF by AA Similarity.
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Explain why ?ABE ?ACD, and then find CD.
Prove triangles are similar.
?A ? ?A by Reflexive Property, and ?B ? ?C since
they are right angles.
Therefore ?ABE ?ACD by AA similarity.
x(9) 5(12)
9x 60
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Explain why ?RSV ?RTU and then find RT.
Prove triangles are similar.
It is given that ?S ? ?T. ?R ? ?R by Reflexive
Property.
Therefore ?RSV ?RTU by AA similarity.
RT(8) 10(12)
8RT 120
RT 15
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Given RS UT, RS 4, RQ x 3, QT 2x 10,
UT 10, find RQ and QT.
RQ 8 QT 20
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Determine if the triangles are similar, if so
write a similarity statement.
Find the missing angles.
Check for proportional sides.
AA Similar ?AEZ ?REB
SAS Similar ?AGU ?BEF
Check for proportional sides.
Check for proportional sides.
SSS Similar ?ABC ?FED
Not Similar
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Determine if the triangles are similar, if so
write a similarity statement.
Check for proportional sides.
Sides do not correspond.
AA Similar ?FGH ?KJH
Not Similar.
Not Similar.
Check for proportional sides.
Check for proportional sides.
Not Similar.
Not Similar.
Not Similar.
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Given ?ABC?EDC, AB 38.5, DE 11, AC 3x
8, and CE x 2, find AC and CE.

1. A
2. B
3. C
4. D

CE x 2
AC 3x 8
AC 2 2
AC 3(2) 8
AC 14
AC 4
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Each pair of triangles below are similar, find x.
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Assignment
Section 11 36