Transcript 4-5 Isosceles and Equilateral Triangles

4-5
Isosceles and
Equilateral Triangles
• The congruent sides of an isosceles
triangle are its legs
• The third side is the base
• The two congruent legs form the vertex
angle
• The other two angles are the base
angles
Isosceles Triangle Theorem
If two sides of a triangle are congruent,
then the angles opposite those sides
are congruent
Converse of the Isosceles Triangle Theorem
If two angles of a triangle are
congruent , then the sides opposite
those angles are congruent
Problem 1: Using the Isosceles Triangle
Theorems
Theorem 4-5
If a line bisects the vertex angle of an
isosceles triangle, then the line is also the
perpendicular bisector of the base
Problem 2: Using Algebra
What is the value of x?
Corollary: is a theorem that can be
proved easily using another theorem.
A corollary is a theorem, so you can
use it as a reason in a proof.
Corollary to Theorem 4-3
If a triangle is equilateral, then
the triangle is equiangular.
Corollary to Theorem 4-4
If a triangle is equiangular, then
the triangle is equilateral.
Problem 3: Finding Angle Measures
What are the
measures of <A, <B,
and <ADC in the
photo?