Page 235 - ABCTE Study Guide_Neat

Angle-Angle (AA) Similarity Theorem: If two angles in one triangle are congruent to two angles in
another triangle, then the triangles are similar. Two figures are similar if they have the same shape, but
not necessarily the same size.

The AA theorem states that only two angles must be congruent for similarity. Do you see why this is true?
Since the sums of the angles in each triangle are equal, if two angles are congruent, then the third
anglesmust also be congruent.

Isosceles Triangle Theorem: If a triangle is isosceles, then the angles opposite the congruent sides are
congruent.

Isosceles Triangle Theorem

Let’s prove this one together. We’ll use the isosceles triangle above ( ) and start by
bisecting with segment .

Statement Justification

is isosceles
Given
is an angle bisector

Definition of Angle Bisector

Definition of Isosceles

Reflexive Property of Congruence