Download Isosceles Triangle Theorem

Lesson 4-4
Isosceles Triangle Theorem
(page 134)
Essential Question
Can you construct a proof
using congruent triangles?
ISOSCELES TRIANGLE: a triangle with at least
two
sides congruent.
congruent sides.
LEGS (of an isosceles triangle): the _______________
third side.
BASE (of an isosceles triangle): the __________
vertex angle: ∠A
A
vertex
angle
leg
base angle
B
base angles: ∠B & ∠C
leg
base angle
base
C
Theorem 4-1
The Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the
angles opposite those sides are congruent.
A
B
Base angles of an isosceles triangle are congruent.
C
Given:
Prove:
A
AB @ AC
∠B ∠C
B
Proof:
Statements
D
Reasons
C
Corollary 1
An equilateral triangle is also
equiangular .
xº
xº
xº
If all 3 sides are congruent, then all 3 angles are congruent.
Corollary 2
An equilateral triangle has three
60 º
60 º
60 º
60º
angles.
Corollary 3
The bisector of the vertex angle of an isosceles
triangle is perpendicular to the base at its
midpoint.
Theorem 4-2
Converse of Theorem 4-1
If two angles of a triangle are congruent, then the
sides opposite those angles are congruent.
Given:
∠B ∠C
Prove:
AB @ AC
A
B
C
Given:
Prove:
A
∠B ∠C
AB @ AC
Proof:
B
D
C
Corollary
An equiangular triangle is also
equilateral .
xº
xº
xº
If all 3 angles are congruent, then all 3 sides are congruent.
Example # 1.
Find the value of “x”.
40 º
3x-5
40º
x + 21
3 x - 5 = x + 21
2 x - 5 = 21
2 x = 26
13
x = _____
Example # 2.
Find the value of “x”.
xº
x + x + 70 = 180
70º
xº
2 x = 110
55
x = _____
Example # 3.
Find the value of “x”.
62º
62º
xº
xº
62
x = _____
Assignment
Written Exercises on pages 137 to 139
RECOMMENDED: 1 to 7 odd numbers, 19
REQUIRED: 9, 14, 16, 22, 24, 27, 33
(use your template to draw the diagram for #33)
Can you construct a proof
using congruent triangles?