Download Chapter 4: Congruent Triangles

Chapter 4: Congruent
Triangles
4.5
Isosceles & Equilateral Triangles
Isosceles Triangles
vertex angle
leg
leg
base angle
base angle
base
Theorem 4-3
• Isosceles Triangle Theorem
– If two sides of a triangle are congruent, then the
angles opposite those sides are congruent.
Theorem 4-4
• Converse of Isosceles Triangle Theorem
– If two angles of a triangle are congruent, then
the sides opposite the angles are congruent.
Theorem 4-5
• The bisector of the vertex angle of an isosceles
triangle is the perpendicular bisector of the
base.
Proof of the Isosceles Triangle Theorem
• Given: XY  XZ , XB bisects YXZ
• Prove: Y  Z
Y
X
B
Z
Example 1
• Explain why the statements are true.
WVS  S
T
U
W
TR  TS
R
V
S
Example
2
M
• Find the value of y.
y
N
O
63
L
Corollary
• a statement that follows immediately from
a theorem
• like a “side note”
Corollaries
• Corollary to Theorem 4-3:
– If a triangle is equilateral, then the triangle is
equiangular.
• Corollary to Theorem 4-4:
– If a triangle is equiangular, then the triangle is
equilateral.
Example 3
• A square and a regular hexagon are placed
so that they have a common side. Find the
following:
mSHA 
S
mHAS 
H
A
Example 4
• Five fences meet at a point to form angles with
measures x, 2x, 3x, 4x, and 5x around the
point. Find the measure of each angle.
Homework
• p. 230
• 1-7, 10-13, 15, 20-22, 28, 30-32