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COPY THEOREMS ON PROOF SHEET THEOREM 5.1: Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. THEOREM 5.2: Any point equidistant from the endpoints of a segment lies on the perpendicular bisector of the segment. THEOREM 5.3 – CIRCUMCENTER THEOREM: The circumcenter of a triangle is equidistant from the vertices of the triangle. THEOREM 5.4: Any point on the angle bisector is equidistant from the sides of the angle. THEOREM 5.5: Any point equidistant from the sides of an angle lies on the angle bisector.

Contents Lesson 5-1Bisectors, Medians, and Altitudes Lesson 5-2Inequalities and Triangles Lesson 5-3Indirect Proof Lesson 5-4The Triangle Inequality Lesson 5-5Inequalities Involving Two Triangles

Lesson 1 Contents Example 1Use Angle Bisectors

Example 1-1a Given: Prove:

Example 1-1a Proof: Statements Reasons Given Angle Sum Theorem Substitution Subtraction Property Definition of angle bisector Angle Sum Theorem Substitution Subtraction Property

Example 1-1b Prove: Given:.

Example 1-1b Proof: Statements. Reasons 1. Given 2. Angle Sum Theorem 3. Substitution 4. Subtraction Property 5. Definition of angle bisector 6. Angle Sum Theorem 7. Substitution 8. Subtraction Property Given

End of Lesson 1

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