5-1 Perpendicular and Angle Bisectors Section 5.1

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Learning Targets Prove and apply theorems about perpendicular bisectors. Prove and apply theorems about angle bisectors.

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5-1 Perpendicular and Angle Bisectors Section 5.1 Holt McDougal Geometry Holt Geometry

Warm Up 1. Find the midpoint and slope of the segment 2. Write the equation of a line that passes through (8,-4) and (5,2).

When a point is the same distance from two or more objects, the point is said to be equidistant from the objects.

A locus is a set of points that satisfies a given condition A locus is a set of points that satisfies a given condition. The perpendicular bisector of a segment can be defined as the locus of points in a plane that are equidistant from the endpoints of the segment.

Find the measure of segment MN. Given that line ℓ is the perpendicular bisector of DE and EG = 14.6, find DG.

Find the measure of segment BC. Given that DE = 20.8, DG = 36.4, and EG =36.4, find EF.

Find the measure of segment TU

Based on these theorems, an angle bisector can be defined as the locus of all points in the interior of the angle that are equidistant from the sides of the angle.

Find the measure of segment BC. Given that YW bisects XYZ and WZ = 3.05, find WX.

Find mEFH, given that mEFG = 50°. Given that mWYZ = 63°, XW = 5.7, and ZW = 5.7, find mXYZ.

Find mMKL.

S is equidistant from each pair of suspension lines S is equidistant from each pair of suspension lines. What can you conclude about QS? QS bisects  PQR.

Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints C(6, –5) and D(10, 1). Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints P(5, 2) and Q(1, –4).

Lesson Quiz: Part I Use the diagram for Items 1–2. 1. Given that mABD = 16°, find mABC. 2. Given that mABD = (2x + 12)° and mCBD = (6x – 18)°, find mABC. Use the diagram for Items 3–4. 3. Given that FH is the perpendicular bisector of EG, EF = 4y – 3, and FG = 6y – 37, find FG. 4. Given that EF = 10.6, EH = 4.3, and FG = 10.6, find EG.

Lesson Quiz: Part II 5. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints X(7, 9) and Y(–3, 5) .