Download 4.2 Properties of Special Triangles

Warm-up
w
1. Find w.
52  x  x  180
52  2 x  180
2 x  128
x  64
w  64  90
w  26
x
52°
x
B
2. Find  A,  B,  C
3x + 28
3x 28 4 x 40 x 48  180
8 x  116  180
8 x  64
x 8
mA  72
mB  52
mC  56
4x + 40
A
x + 48
C
4.2 Properties of
Special Triangles
Year 2 Geometry
Investigation #1(optional)
Draw an angle on patty paper. Label the
angle C.
 Put point A on one ray.
 Fold the patty paper so both rays match.
 Copy point A on the other ray and label it
B.
 Construct line segment AB.

Investigation #1 continued





What type of triangle is this? ISOSCELES!
How can you tell? TWO SIDES ARE CONGRUENT!
Name the vertex angle. ACB
Name the base. AB
Name the base angles (2). CAB, CBA
Isosceles Triangle Conjecture

If a triangle is isosceles, then its base
CONGRUENT
angles are ______________?
Base angles
Converse of the Isosceles Triangle
Conjecture

If a triangle has two congruent angles,
then
THE TRIANGLE IS ISOSCELES
_________________________________?
Example #1
70°
x
x
Find x.
70  x  x  180
70  2 x  180
2 x  110
x  55
Example #2
x  24
24  24  y  180
48  y  180
Find x and y.
y
y  132
24°
x
Example #3

Find x and the
measure of each
angle.
2 x  9  2 x  9  6 x  22  180
10 x  40  180
10 x  140
x  14
2x  9
37°
2x  9
106°
6x  22
37°
Wonderful Example #4
Find the missing angles
e
h
63°
f
g
a=122° b=58°
c=58°
d=39°
h=102° k=78°
n=83°
p=39°
b
a
k
58°
d
e=39°
f=78°
c
n
g=63°
p
Summary

Rewrite the Isosceles Triangle Conjecture
and the Converse of the Isosceles Triangle
Conjecture in your own words.
Homework

Classwork
 Worksheet

Homework
 Pg
206 1-8, 10,11, 21, 22