Download 3.1 What are congruent figures?

3.7 Angle-Side Theorems
Objective:
After studying this lesson you will be able to
apply theorems relating the angle measures
and side lengths of triangles.
Theorem:
if two sides of a triangle are congruent, the
angles opposite the sides are congruent.
If
, then
C
Given: CA  CT
Prove: A  T
Statement
A
Reason
1.
1.
2.
2.
3.
3.
4.
4.
T
Theorem:
if two angles of a triangle are congruent,
then sides opposite the angles are congruent.
If
, then
Y
B
Given: B  Y
Prove: OY  OB
O
Statement
Reason
1.
1.
2.
2.
3.
3.
4.
4.
Theorem:
If two sides of a triangle are not
congruent, then the angles opposite them
are not congruent, and the larger angle is
opposite the longest side.
80
60
40
Longest side
Theorem:
If two angles of a triangle are not
congruent, then the sides opposite them
are not congruent, and the larger side is
opposite the larger angle.
Given: AC  AB
mB  mC  180
mB  6x  45
mC  15  x
What are the restrictions on x?
A
(6x-45)
B
(15+x)
C
Prove: The bisector of the vertex angle of an
isosceles triangle is also the median to the base.
O
Statement
Reason
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.
8.
8.
J
K
M
T
Given: 3  4
BX  AY
BW  AZ
B
3
4
A
Prove: WTZ is isosceles
Statement
Reason
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.
8.
8.
9.
9.
W
X
Y
Z
D
Given: E  H
EF  GH
Prove: DG  DF
Statement
Reason
1.
1.
2.
2.
3.
3.
4.
4.
E
F
G
H
Summary:
Where is the longest side
located? The shortest?
If base angles are
congruent what can we
say about the triangle?
Homework: worksheet