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Geometry Ms. Stawicki

1) To use and apply properties of isosceles triangles

The congruent sides of an isosceles triangle are its legs. The third side is the base. The two congruent sides form the vertex angle. The other two angles are the base angles. Vertex angle Leg Base Base Angle

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 Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite the angles are congruent. A BC A BC

Theorem 4-5: The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. C AB D

Corollary: a statement that follows immediately from a theorem. In other words, taking a theorem one step further to apply to something else that follows the same concept of the theorem…. ▪ In this case, we are taking the Isosceles Triangle Theorems & applying them to EQUILATERAL TRIANGLES

Corollaries to the Isosceles Triangle Theorem & its converse: 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

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