http://www.ck12.org Chapter 4. Triangles and Congruence
Isosceles Triangle Theorem Converse:The perpendicular bisector of the base of an isosceles triangle is also the
angle bisector of the vertex angle.
In other words, if 4 ABCis isosceles,AD⊥CBandCD∼=DB, then^6 CAD∼=^6 BAD.
Example A
Which two angles are congruent?
This is an isosceles triangle. The congruent angles, are opposite the congruent sides.
From the arrows we see that^6 S∼=^6 U.
Example B
If an isosceles triangle has base angles with measures of 47◦, what is the measure of the vertex angle?
Draw a picture and set up an equation to solve for the vertex angle,v.
47 ◦+ 47 ◦+v= 180 ◦
v= 180 ◦− 47 ◦− 47 ◦
v= 86 ◦Example C
If an isosceles triangle has a vertex angle with a measure of 116◦, what is the measure of each base angle?
Draw a picture and set up and equation to solve for the base angles,b. Recall that the base angles are equal.
116 ◦+b+b= 180 ◦
2 b= 64 ◦
b= 32 ◦Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter4IsoscelesTrianglesB
Vocabulary
An isosceles triangle is a triangle that hasat leasttwo congruent sides. The congruent sides of the isosceles triangle
are called thelegs. The other side is called thebase. The angles between the base and the legs are calledbase
angles. The angle made by the two legs is called thevertex angle.