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.

Theorem 4.3 - Isosceles Triangle Theorem

• If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Theorem 4.4 – 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 Theoremsa. Is segment AB congruent to segment CB? Explain.Yes, since angle C is congruent to angle A, then segment AB is

congruent to segment CB.b. Is angle A congruent to angle DEA? Explain. Yes, since segment AD is congruent to segment ED, then

angle A is congruent to angle DEA.

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?

180m C m BDC m DBC 54 90 180x

144 180x 36x

Corollary

• A corollary is a theorem that can be proved easily using another theorem.– Since a corollary is a theorem, 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.

More Practice!!!!!

• Homework – Textbook p. 253 – 254 #1 – 13, 16 – 19.