Theorems: Isosceles Triangles

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Presentation transcript:

Theorems: Isosceles Triangles Isosceles Triangles have two congruent sides (legs) and a third side (base) leg leg base

Isosceles Triangle Vertex angle The angles at the base are called base angles and the angle opposite the base is the vertex angle Base angles

What we know about them: P <PRS cong. <PSR Seg.PQ bisects <RPS Seg.PQ bisects Seg.RS Seg.PQ is perp. to Seg.RS at Q Triangle PQR is congruent to Triangle PQS R Q S

Isosceles Triangle Theorem P If two sides of a triangle are congruent, then the angles opposite those sides are congruent. In other words, if PR is congruent to PS, then <R is congruent to <S R Q S

Isosceles Triangle Corollaries P An equilateral triangle is also equiangular An equilateral triangle has three 60 degree angles. The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint. R S Q

Theorem 4-2 P If two angles of a triangle are congruent, then the sides opposite those angles are congruent. R S Q

Corollary An equiangular triangle is also equilateral.