Download 4-5 Isosceles and Equilateral Triangles

4-5 Isosceles and Equilateral
Triangles
Isosceles Triangles
• The congruent sides of an isosceles triangle
are its legs.
• The third side is the base.
• The legs form the vertex angle.
• The other two angles are the base angles.
Isosceles Triangle Theorems
Isosceles Triangle Theorem: If two sides of a
triangle are congruent, then the angles
opposite those sides are congruent.
(Also known as the Base Angles Theorem)
Converse of the Isosceles Triangle Theorem: If
two angles of a triangle are congruent, then
the sides opposite those angles are congruent.
Using the Isosceles Triangle Theorems
• Is AB congruent to CB? Explain.
• Is A congruent to DEA? Explain.
Answer the following:
• Is WVS congruent to S? Explain.
• Is TR congruent to TS? Explain.
Bisectors
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.
Using Algebra
• What is the value of x?
Suppose mA = 27. What is the value of x?
Corollaries
• A corollary is a theorem that can be proved
easily using another theorem.
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.
Finding Angle Measures
• What are the measures of
A, B, and ADC?