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More Lessons for Geometry

Common Core For Geometry

Worksheets for Geometry, Module 2, Lesson 18

Student Outcomes

- Students state, understand, and prove the Angle Bisector Theorem.
- Students use the Angle Bisector Theorem to solve problems.

**Similarity and the Angle Bisector Theorem**

Classwork

**Opening Exercise**

a. What is an angle bisector?

b. Describe the angle relationships formed when parallel lines are cut by a transversal.

c. What are the properties of an isosceles triangle?

**Discussion**

In the diagram below, the angle bisector of β π΄ in β³ π΄π΅πΆ meets side π΅πΆΜ Μ Μ Μ at point π·. Does the angle bisector create any observable relationships with respect to the side lengths of the triangle

**Exercises 1β4**

- The sides of a triangle are 8, 12, and 15. An angle bisector meets the side of length 15. Find the lengths π₯ and π¦. Explain how you arrived at your answers.
- The sides of a triangle are 8, 12, and 15. An angle bisector meets the side of length 12. Find the lengths π₯ and π¦.
- The sides of a triangle are 8, 12, and 15. An angle bisector meets the side of length 8. Find the lengths π₯ and π¦.
- The angle bisector of an angle splits the opposite side of a triangle into lengths 5 and 6. The perimeter of the triangle is 33. Find the lengths of the other two sides.

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