Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,

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Welcome to Interactive Chalkboard

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Welcome to Interactive Chalkboard

Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,

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NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3. Any point that is on the perpendicular bisector of a segment is equidistant from the endpoints of the.

5.1 Bisectors, Medians, and Altitudes. Objectives Identify and use ┴ bisectors and  bisectors in ∆s Identify and use medians and altitudes in ∆s.

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 Perpendicular Bisector- a line, segment, or ray that passes through the midpoint of the side and is perpendicular to that side  Theorem 5.1  Any point.

Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,

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Medians, and Altitudes.

Bisectors, Medians, and Altitudes

Medians, Altitudes and Perpendicular Bisectors

Bisectors, Medians and Altitudes

Medians and Altitudes Median – A segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite the vertex. Centroid – The point.

Welcome to Interactive Chalkboard

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

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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

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.

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

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

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.

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.

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:

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

End of Lesson 1

End of Slide Show