2. Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio 45202 Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

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4. 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.

5. 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

6. Lesson 1 Contents Example 1Use Angle Bisectors

7. Example 1-1a Given: Prove:

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

9. Example 1-1b Prove: Given:.

10. 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 1. 2. 3. 4. 5. 6. 7. 8. 1. Given

11. End of Lesson 1

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