Download 8.3: Proving Triangles Similar

8.3: Proving Triangles Similar
Objectives:
•To use and apply AA, SAS and SSS similarity statements
•To use indirect measurement and proportions to find
missing measures
Angle-Angle Similarity (AA~)Postulate
If two angles of one triangle are congruent
to two angles of another, then the triangles
are similar
LMK ~ IJH
Side-Angle-Side Similarity (SAS~)
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.
E
B
ABC ~ DEF
A
D
C
F
Side-Side-Side Similarity (SSS~)
Theorem
If the corresponding sides of 2 triangles are
proportional, then the triangles are similar.
6
6
3
8
8
4
Explain why the triangles must be similar. Then write a
similarity statement.
T
J
C
G
K
Z
Are the triangles similar? If so, write a similarity statement
and name the postulate or theorem you used.
1. (not drawn to scale)
A
10
X
30
B
25
Y
75
C
2.
Explain why the triangles are similar. Then find x.
1.
x
24
14
22
Are the two triangles similar? If so, state the theorem or
postulate and write a similarity statement
.
Are the 2 triangles similar?
Indirect Measurement
Use similar triangles and measurements
to find distances that are difficult to
measure directly
 Fact: light reflects off a mirror at the
same angle at which it hits mirror
(creating similar triangles)
 Fact: similar triangles are formed by
certain figures and their shadows

Example:
1. A fire hydrant 2.5 feet high casts a 5-foot
shadow. How tall is a street light that casts a 26foot shadow at the same time? Let h represent the
height of the street light.
2. At 7 feet 2 inches, Margo Dydek is one of the tallest
women to play professional basketball. Her coach,
Carolyn Peck, is 6 feet 4 inches tall. If Ms. Peck casts a
shadow that is 4 feet long, about how long would Ms.
Dydek’s shadow be? Round to the nearest tenth.