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Perpendiculars and Bisectors Theorems in Geometry

Understand the properties of perpendiculars and bisectors in segments and angles in geometry. Learn about equidistance and the relationship between points, segments, and angles.

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Perpendiculars and Bisectors Theorems in Geometry

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  1. 5.1 Perpendiculars and Bisectors

  2. Perpendicular Bisector Theorem • If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. • If CP is the perpendicular bisector of AB, then CA = CB. C B P A

  3. Converse of the Perpendicular Bisector Theorem • If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. • If CA=CB, then C lies on the perpendicular bisector of

  4. In the diagram shown, MN is the perpendicular bisector of ST. • What segment lengths in the diagram are equal? • Explain why Q is on MN T 12 Q N M 12 S

  5. Angle Bisector Theorem • If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. • If m<BAD = m<CAD, then DB = DC. B D A C

  6. Converse of the Angle Bisector Theorem • If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle. • If DB=DC, then m<BAD = m<CAD

  7. Use the diagram to answer the following. In the diagram, F is on the bisector of < DAE. • If m<BAF = 50, then m<CAF = ____ • If FC = 10, then FB = ____ • Is triangle ABF congruent to triangle ACF? Explain. A B C E D F G

  8. Closing Question:

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