Isosceles Triangle Theorem and its Converse
Isosceles Triangle Theorem and its Converse
[size=100]In an isosceles triangle, two sides ([u]legs[/u]) of the triangle are congruent. In the isosceles triangle below, sides AB and AC are the congruent legs. BC is the [u]base[/u]. Angle A is the [u]vertex angle[/u] (opposite the base) and Angles B and C are the [u]base angles[/u].[br][br]Move the vertices of the isosceles triangle, and identify the relationship between the sides and angles of the isosceles triangle. [br][/size]
[size=100]1. What do you notice about the base angles (Angle B and Angle C) of the isosceles triangle ABC, as you move the vertices of the triangle. [/size]
[size=150][u][b]Isosceles Triangle Theorem[/b]:[/u] If [u]two sides[/u] of a triangle are CONGRUENT, the angles [u]opposite[/u] are CONGRUENT.[br][/size] or[br][b]BASE [/b]angles of an isosceles triangle are CONGRUENT[br][br]The [b]converse [/b]is also [b]TRUE[/b]. [br][br][u][b]Converse of the Isosceles Triangle Theorem[/b]:[/u] If [u]two angles[/u] of a triangle are CONGRUENT, the sides [u]opposite[/u] are CONGRUENT.
2. In triangle ABC, side AB is congruent to side AC.
Make another congruent statement about triangle ABC.
3. In triangle SAM, angle S is congruent to angle A.
Make another congruent statement about triangle SAM.