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Prove and apply theorems about perpendicular bisectors.

Explore and apply theorems related to perpendicular and angle bisectors in geometry. Learn vocabulary like equidistant locus and triangle congruence theorems to prove theorems about equidistant points. Utilize examples to understand concepts thoroughly.

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Prove and apply theorems about perpendicular bisectors.

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  1. Objectives Prove and apply theorems about perpendicular bisectors. Prove and apply theorems about angle bisectors.

  2. Vocabulary equidistant locus

  3. When a point is the same distance from two or more objects, the point is said to be ____________from the objects. Triangle congruence theorems can be used to prove theorems about equidistant points.

  4. A ________ 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.

  5. Example 1A: Applying the Perpendicular Bisector Theorem and Its Converse Find each measure. MN

  6. Example 1B: Applying the Perpendicular Bisector Theorem and Its Converse Find each measure. BC

  7. Example 1C: Applying the Perpendicular Bisector Theorem and Its Converse Find each measure. TU

  8. Remember that the distance between a point and a line is the length of the perpendicular segment from the point to the line.

  9. Example 2A: Applying the Angle Bisector Theorem Find the measure. BC

  10. Example 2B: Applying the Angle Bisector Theorem Find the measure. mEFH, given that mEFG = 50°.

  11. Example 2C: Applying the Angle Bisector Theorem Find mMKL.

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