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5.1 Perpendiculars and Bisectors

Learn to apply properties of perpendicular bisectors to identify equal distances. Study perpendicular and bisectors theorems for segments, rays, and angles. Equidistant relationships and examples included. Review assignments from pages 267-269. 8

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5.1 Perpendiculars and Bisectors

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  1. Obj. SWBAT use properties of perpendicular bisectors to find/identify equal distances 5.1 Perpendiculars and Bisectors

  2. Theorems • Perpendicular Bisector – segment/ray/line that intersects a segment at the midpoint in a right angle. • Perpendicular Bisector Thm – If a point is on the perpendicular bisector of a segment, then it is equidistant to the endpoints (ex. CA = CB)‏

  3. Another Theorem • Angle Bisector – a line/ray/segment which splits an angle into 2 equal parts. • Angle Bisector Thm – If a point is on the bisector of an angle, then it is equidistant from the two sides of an angle (If <ABD = <DBC, then AD = DC)‏ • *For converse to work, segments must be perpendicular to rays.

  4. Examples • Is P on the angle bisector of A? YES NO

  5. Example 3 • MP is the perpendicular bisector of LN. What is the relationship between LP and PN? • They are equal

  6. Assignment • p. 267-269 1-13, 16-26, 33-34 all

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