4-5 isosceles and equilateral triangles. the congruent sides of an isosceles triangle are its legs...
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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 4-5If 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 MeasuresWhat are the measures of <A, <B, and <ADC in the photo?