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Isosceles and Equilateral Triangles
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Isosceles Triangle – Triangle with two congruent sides.
• The congruent sides are the legs.
• The third side is the base.
• The two legs form the vertex angle.
• The other two angles are the base angles.
• Legs of an isosceles triangle are congruent.
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Base angles of an isosceles triangle are congruent.
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are
congruent.
Proof of Isosceles Triangle Theorem
Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are
congruent.
Theorem: If a line bisects the vertex angle of an isosceles triangle, then the line is also
the perpendicular bisector of the base.
Equilateral Triangle – Triangle with three congruent sides.
Corollary – A theorem that can be proved using another theorem.
Corollary – If a triangle is equilateral, then the triangle is equiangular.
Corollary – If a triangle is equiangular, then the triangle is equilateral.
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4. Find the 𝑚∠𝐴𝐶𝐵
5. Find the 𝑚∠𝐷𝐵𝐶
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6. Find the 𝑚∠𝐴𝐵𝐶