5.4 – EQUILATERAL AND ISOSCELES

TRIANGLES

USING THE BASE ANGLES THEOREM

A triangle is isosceles when it has at least two congruent sides.The congruent sides are called the legsThe angle formed by the legs is called the vertex angle.The third side is the baseThe Two angles adjacent to the base are called the base angles.

THEOREM 5.6 – BASE ANGELS THEOREMIf two sides of a triangle are congruent, then the angles opposite them are congruent

If

THEOREM 5.7 – CONVERSE OF THE BASE ANGLES THEOREMIf two angels of a triangle are congruent, then the sides opposite them are congruent.

If

EXAMPLE 1 – USING THE BASE ANGELS THEOREM

YOU TRY

HGK HKG

HK JK

COROLLARIRES

EXAMPLE 2 – FINDING MEASURES IN A TRIANGLE

YOU TRY!

SOLUTIONBecause the triangle is equiangular, it is also equilateral, meaning all of the side lengths are equal.Therefore, the length of ST is also 5.

EXAMPLE 3 – USING ISOSCELES AND EQUILATERAL TRIANGELS

YOU TRY!

SOLUTIONX = 60Y = 120