http://www.ck12.org Chapter 4. Triangles and Congruence
Base Angles Theorem Converse: If two angles in a triangle are congruent, then the opposite sides are also
congruent.
So, for a triangle 4 ABC, if^6 A∼=^6 B, thenCB∼=CA.^6 Cwould be the vertex angle.
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.