4-6 Isosceles, Equilateral and Right Triangles

4-6Isosceles, Equilateral and Right Triangles

Parts of Isosceles Triangles Legs of an Isosceles Triangle – The congruent sides of an isosceles triangle Base of an Isosceles Triangle – The non-congruent side of an isosceles triangle Vertex Angle – The angle formed by the legs in an isosceles triangle Base Angles – The angles opposite the legs in an isosceles triangle

H Vertex Angle Leg Leg Base Angles P I Base

The Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent If two angles of a triangle are congruent, then the sides opposite those angles are congruent

Informal Proof of the Isosceles Triangle Theorem: H • Draw auxiliary segment that bisects • Two triangles are congruent by • by SSS CPCTC I P H • Draw auxiliary segment that bisects • Two triangles are congruent by • by AAS CPCTC P I

Corollary - A true statement that follows immediately from a theorem • Corollaries following the Isosceles Triangle Theorem • If a triangle is equilateral, then it is equiangular • If a triangle is equiangular, then it is equilateral

Parts of Right Triangles Hypotenuse of a Right Triangle – The side opposite the right angle in a right triangle Legs of a Right Triangle – The sides that form the right angle in a right triangle D Hypotenuse Leg J M Leg

Hypotenuse-Leg Theorem HL Theorem If the hypotenuse and the leg of a right triangle are congruent to the hypotenuse and the leg of another right triangle, then the two triangles are congruent

Informal Proof of the HL Theorem: ● • Draw auxiliary . Mark point S so that . • by • by • by • by • by SAS CPCTC CPCTC AAS Theorem

4-6 Isosceles, Equilateral and Right Triangles