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Geometry

Geometry. 5-3 Use Angle Bisectors of Triangles. Learning Target. We will identify and use angle bisectors to find distance relationships. From yesterday’s lesson.

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Geometry

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  1. Geometry 5-3 Use Angle Bisectors of Triangles

  2. Learning Target • We will identify and use angle bisectors to find distance relationships.

  3. From yesterday’s lesson • Concurrency of perpendicular bisectors of a triangle: the point where the perpendicular bisectors meet will be the same distance from each vertices. • Picture is on page 305

  4. Angle Bisector Theorem • Theorem 5.5: Any point on the angle bisector is equidistant from the sides of the angle. • Theorem 5.6: (Converse) Any point equidistant from the sides of an angle lies on the angle bisector. X Y Z

  5. Examples Page 310-311 • Ex 1: Find the measure of angle GFJ • Ex 2: Does the goalie have to move one way more? • Ex 3: Find x • Guided Practice 1-4

  6. Concurrency of Angle Bisectors of a Triangle • The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle. (The perpendicular bisectors will meet and be the same distance of each other at the place where the angle bisectors meet.) • Picture in book on page 312

  7. Perpendicular bisectors and angle bisectors (cont’d) • Incenter: The point of concurrency of the angle bisectors of a triangle. A P R F E incenter M B C Q D If M is the incenter, then MP = MQ = MR.

  8. Examples of concurrency of angle bisectors • Example 4 Page 312 • Guided practice #5

  9. Together • Page 313 #3, 5, 7, 9, 11, 13, 15, 19-20,

  10. Homework • Page 313 #4-20 even, 24

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