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. 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

5. COPY THEOREMS ON PROOF SHEET THEOREM 5.6 – INCENTER THEOREM: The incenter of a triangle is equidistant from each side of the triangle. THEOREM 5.7 – CENTROID THEOREM: The centroid of a triangle is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median.

6. Lesson 1 Contents Example 2Segment Measures OBJECTIVE: To identify and use medians and altitudes in triangles (2.9.8D) (M8.C.1.1)

7. Example 1-2a ALGEBRA Points U, V, and W are the midpoints of respectively. Find a, b, and c.

8. Example 1-2a Find a. Segment Addition Postulate Centroid Theorem Substitution Multiply each side by 3 and simplify. Subtract 14.8 from each side. Divide each side by 4.

9. Example 1-2a Find b. Segment Addition Postulate Centroid Theorem Substitution Multiply each side by 3 and simplify. Subtract 6b from each side. Divide each side by 3. Subtract 6 from each side.

10. Example 1-2a Find c. Segment Addition Postulate Centroid Theorem Substitution Multiply each side by 3 and simplify. Subtract 30.4 from each side. Divide each side by 10. Answer:

11. ALGEBRA Points T, H, and G are the midpoints of respectively. Find w, x, and y. Example 1-2b Answer:

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