http://www.ck12.org Chapter 4. Triangles and Congruence
Because 4 DEG∼= 4 F EG, we know that^6 EGD∼=^6 EGFby CPCTC. Thes two angles are also a linear pair, so
they are congruent supplements, or 90◦each. Therefore,EG⊥DF.
Additionally,DG∼=GFby CPCTC, soGis the midpoint ofDF. This means thatEGis theperpendicular bisector
ofDF, in addition to being the angle bisector of^6 DEF.
Isosceles Triangle Theorem:The angle bisector of the vertex angle in an isosceles triangle is also the perpendicular
bisector to the base.
This is ONLY true for the vertex angle.We will prove this theorem in the review questions for this section.
Example 1:Which two angles are congruent?
Solution:This is an isosceles triangle. The congruent angles, are opposite the congruent sides.
From the arrows we see that^6 S∼=^6 U.
Example 2:If an isosceles triangle has base angles with measures of 47◦, what is the measure of the vertex angle?
Solution:Draw a picture and set up an equation to solve for the vertex angle,v.