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**5-1 Special Segments in Triangles**

Objective: Use medians, angle bisectors, perpendicular bisectors and altitudes to solve problems. RELEVENCE: Construction

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**Perpendicular Bisector of a Triangle**

A line or line segment that passes through the midpoint of a side of a triangle and is perpendicular to that side. Perpendicular Bisector

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Median of a Triangle A segment that joins a vertex of the triangle and the midpoint of the opposite side. Median

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Altitude of a Triangle A segment from a vertex of the triangle to the line containing the opposite side and perpendicular to the line containing that side. Altitude

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**Angle Bisector of a Triangle**

A segment that bisects an angle of the triangle and has one endpoint at a vertex of the triangle and the other endpoint at another point on the triangle. Angle Bisector

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**Example 1: If SU is a median of ∆RST, find SR. S 4x + 11 T R 3x + 7 U**

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**Example 2: If GM is an angle bisector, find m∠IGM. I M (x + 12)° G H**

m∠IGH = (3x – 5)°

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**Exit Ticket Find BC if CD is a median of ∆ABC. C 3x + 8 A 4x + 5 D**

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1 Def: Median Def: A median of a triangle is a line segment that joins any vertex of the triangle to the midpoint of the opposite side. Every triangle.

1 Def: Median Def: A median of a triangle is a line segment that joins any vertex of the triangle to the midpoint of the opposite side. Every triangle.

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