Download The Base Angles Theorem

Students:
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P
PR and QR
PQ
1) Identify the legs
2) Identify the base
R
3) Identify the base angles  P and  Q
Q
A
4) Find m  C = 55
5) Find m  A
55°
B
= 70
C
y°
x°
50°
6) Find x
= 80
7) Find y
= 50
10.02
Converse of the
Base Angles
Theorem
The Base Angles Theorem
If two sides of a triangle are congruent, then
the angles opposite those sides are congruent.
A
If AB  AC , then  B   C
B
C
Converse of the Base Angles Theorem
If two angles of a triangle are congruent, then
the sides opposite those angles are congruent.
A
If  B   C , then AB  AC
B
C
Determine which sides are congruent.
R
A
45°
P
B
45°
C
Q
PQ  PR
AB  BC
D
L
M
E
DE  EF
N
F
LM  MN  LN
Find the length of the missing side.
R
45°
A
6 cm
P
6m
5 cm
8.5 m
45°
B
C
Q
BC = 5 cm
PR =
D
EF = 8 cm
11 cm
8 cm
E
F
6m
Solve for x and find the missing sides.
B
x= 3
7x + 15
13x + 9
A
57°
66°
10x + 6
Find
B
 B  57
AC  BC
C
AB = 13(3) + 9
= 48
BC = 7(3) + 15
= 36
AC = 10(3) + 6
= 36
10x + 6 = 7x + 15
3x + 6 = 15
3x = 9