Download Isosceles Triangle Theorem

November 10, 2016
Unit 4, Lesson 6
Isosceles Triangle
Theorem
"Mighty is geometry; joined with art, resistless."
- Euripides
Example 1:
A
A
(hint: What is a congruence statement we can write?)
B
C
B
C
November 10, 2016
Example 2:
A
A
C
B
B
How are Examples 1 and 2 related?
What is true if a triangle has two congruent sides?
What if two angles are congruent?
C
November 10, 2016
Isosceles Triangle Theorem ( Theorems 4-1 and 4-2)
Two sides of a triangle are congruent if and only if
the angles opposite those sides are congruent.
Parts of an Isosceles Triangle:
Legs - two congruent sides
Base - the third side
Base Angles - Angles formed with base
Vertex Angle - Angle opposite base
November 10, 2016
Corollary 1 to Isos. Triangle Theorem
A triangle is equilateral if and only if it is equiangular
Corollary 2 to Isos. Triangle Theorem
o
An equilateral triangle has three 60 angles.
November 10, 2016
Corollary 3 to Isos. Triangle Theorem
The bisector of the vertex angle of an isosceles triangle
is perpendicular to the base at its midpoint.
Example 3: Find the measure of angle A.
November 10, 2016
Example 4: Find the measure of angle BOC. O is the center
of the circle.
(hint: what do you know about the radii of a circle, and let
Example 5:
)
November 10, 2016
Example 6:
Explain why all equilateral triangles are isosceles triangles but
not all isosceles triangles are equilateral triangles.