Download 4.7 Use Isosceles and Equilateral Triangles

4.7 Use Isosceles and Equilateral Triangles
Goal  Use theorems about isosceles and equilateral triangles.
VOCABULARY
Legs - The legs of an isosceles triangle are the two congruent sides.
Legs
Vertex angle - The vertex angle of an isosceles triangle is the angle formed by the legs.
Base - The base of an isosceles triangle is the side that is not a leg.
Base angles - The base angles of an isosceles triangle are the two angles adjacent to the
base.
Base s
BASE ANGLES THEOREM
If two sides of a triangle are congruent,
then the angles opposite them are congruent.
If
then
If AB  AC , then B  ____.
CONVERSE OF BASE ANGLES THEOREM
If two angles of a triangle are congruent,
then the sides opposite them are congruent.
If
then
If B  C, then AB  _____.
Example
Apply the Base Angles Theorem
In FGH, FH  GH . Name two congruent angles.
COROLLARY TO THE BASE ANGLES
THEOREM
If a triangle is equilateral, then it is _____________.
COROLLARY TO THE CONVERSE OF
BASE ANGLES THEOREM
If a triangle is equiangular, then it is _____________.
The corollaries state that
a triangle is equilateral
if and only if it is
equiangular.
= sides
= s
Example Find measures in a triangle
Find the measures of R, S, and T.
(All sides are =, so all s are =)
Examples Use isosceles and equilateral triangles
Find the values of x and y.
Find the values of x and y in the diagram.