Download Similarity Theorem

8.3 C
8.4 C
Proving Triangles Similar
Students will be able to prove
triangles similar using the AA,
SSS, SAS similarity theorem.
Given: VW //YZ
Prove: WVX ~ ZYX
W

Statements
1. VW || YZ
2. V  Y
3. VXW  YXZ
4. WVX ~ ZYX

V
X
Z
Reasons
Y
1. Given
2. Alternate Interior Angles Theorem
3. Vertical Angles
4. A - A Postulate
Given: ABC is a right triangle,
B
AD is an altitude
Prove: ABC  DAC
A
Reasons
Statements
1. ABC is a right triangle,
AD is an altitude,
D
1. Given
mBAC = 90 0
2. ADC is right angle
3. mADC = 90 0
4. C = C
5. ABC ~ DAC
2.
3.
4.
5.
Definition of altitude
Definition of right angle
Reflexive Prop
A - A postulate
C
Theorem 8.2 Side-Side-Side
(SSS) Similarity Theorem
If the corresponding sides of two triangles
are proportional, then the triangles are
similar.
AB BC CA
If
, then ABC  PQR.


PQ
QR
RP
Q
B

A
C
P
R
Theorem 8.3 Side-Angle-Side
(SAS) Similarity Theorem
If an angle of one triangle is congruent to an angle
of a second triangle and the lengths of the sides
including these angles are proportional, then the
triangles are similar.
ZX
XY
If X  M and
, then XYZ  MNP.

PM
MN
Y
N

M
X
Z
P
State if the triangles in each pair are similar. If
so, state how you know they are similar and
complete the similarity statement.
similar; SSS similarity; FGH
State if the triangles in each pair are similar. If
so, state how you know they are similar and
complete the similarity statement.
similar; SAS similarity; UVW
State if the triangles in each pair are similar. If
so, state how you know they are similar and
complete the similarity statement.
similar; SSS similarity; FRS
State if the triangles in each pair are similar. If
so, state how you know they are similar and
complete the similarity statement.
not similar