Transcript Area

Similar Triangles 8.3
• Identify similar triangles.
• Learn the definition of AA, SAS, SSS similarity.
• Use similar triangles to solve problems.
homework
homework
homework
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.
homework
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.
homework
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.
homework
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.
homework
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.
homework
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.
homework
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.
AB AC

BE CD
9 12

5 x
x(9) = 5(12)
9x = 60
homework
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
homework
Given RS || UT, RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10,
find RQ and QT.
Since
because they are
alternate interior angles. By AA Similarity, ΔRSQ ~ ΔTUQ. Using the
definition of similar polygons,
RQ = 8; QT = 20
Determine if the triangles are similar, if so
write a similarity statement.
100
35
45
Find the missing angles.
Check for proportional sides.
AA Similar AEZ ~ REB
SAS Similar AGU ~ BEF
2
3
4

.
6

.
6
 .6 Check for proportional sides.
Check for proportional sides.
3
4.5
6
32
45
60
SSS Similar ABC ~ FED
 1.45
 1.5
 1.5
22
30
40
Not Similar
16
12
 .8
 .8
20
15
homework
Determine if the triangles are similar, if so
write a similarity statement.
Sides do not correspond.
Not Similar.
Check for proportional sides.
Vertical angles.
24
32
48
 1.3
 1.3
 1.26
18
24
38
Alternate Interior angles.
Not Similar.
AA Similar FGH ~ KJH
120
45
Check for proportional sides.
Check for proportional sides.
32
45
60
 1.45
 1.5
 1.5
22
30
40
Find the missing angles.
Not Similar.
Not Similar.
6
10
2
 2. 5
3
4
Not Similar.
homework
Given ABC~EDC, AB = 38.5, DE = 11, AC = 3x + 8, and
CE = x + 2, find AC and CE.
38.5 3x  8

11
x2
38.5x  77  33x  88
5.5x  11
x2
AC = 3x + 8
AC = 3(2) + 8
AC = 14
CE = x + 2
AC = 2 + 2
AC = 4
1.
2.
3.
4.
A
B
C
D
homework
Each pair of triangles below are similar, find x.
2x 8

9 x
2x  72
2
x 2  36
x6
2x  4
39

24
x6
2x 2  8x  24  936
2x 2  8x  960  0
x 2  4x  480  0
(x  24)(x  20)  0
homework
x  20
homework
homework
Assignment
Section 11 – 36