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Understanding Bisectors in Triangles: Theorems and Examples

This chapter delves into bisectors in triangles, focusing on perpendicular and angle bisectors. The Perpendicular Bisector Theorem states that a point on the perpendicular bisector of a segment is equidistant from the segment's endpoints. The converse affirms that any point equidistant from endpoints lies on the bisector. Additionally, the Angle Bisector Theorem highlights that a point on the angle bisector is equidistant from the angle's sides, with its converse also validated. By exploring various examples and exercises, this section reinforces comprehension through practical application.

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Understanding Bisectors in Triangles: Theorems and Examples

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  1. Chapter 5: Relationships within Triangles 5.2 Bisectors in Triangles

  2. A little vocab… • perpendicular bisector: • equidistant: • angle bisector:

  3. Theorem 5-2 & 5-3 • Perpendicular Bisector Theorem • If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment • 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

  4. Example 1 • Use the information given in the diagram. CD is the perpendicular bisector of AB. Find CA and DB.

  5. Theorem 5-4 & 5-5 • Angle Bisector Theorem • If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle • Converse of the Angle Bisector Theorem • If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector

  6. Example 2 • What is the length of FD?

  7. Example 3 • Find the value of x, CG, and the perimeter of quadrilateral ABCG.

  8. Homework

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