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5.3 Use Angle Bisectors of Triangles

5.3 Use Angle Bisectors of Triangles. Hubarth Geometry. Angle Bisector Theorem. If. then. C. 1. B. A. 2. 1. B. A. 2. D. Ex 1 Use the Angle Bisector Theorem. Find the measure of  GFJ. For what value of x does P lie on the bisector of A ?. CP. BP =. 2 x – 1.

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5.3 Use Angle Bisectors of Triangles

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  1. 5.3 Use Angle Bisectors of Triangles Hubarth Geometry

  2. Angle Bisector Theorem If then C . 1 B A . 2 1 B A 2 D

  3. Ex 1 Use the Angle Bisector Theorem Find the measure of GFJ.

  4. For what value of xdoes Plie on the bisector of A? CP BP = 2x –1 x + 3 = 4 = x Point Plies on the bisector of Awhen x = 4. Ex 2 Use Algebra to Solve a Problem Set segment lengths equal. Substitute expressions for segment lengths. Solve for x.

  5. Concurrency of Angle Bisector of a Triangle The angle bisector of a triangle intersects at a point that is equidistant from the sides of a triangle. B D E A F C

  6. In the diagram, Nis the incenter of ABC. Find ND. 2 2 2 a + b c = 400 = 2 NF + 256 2 144 = NF 12 = NF 2 2 2 20 = NF + 16 Ex 3 Use the Concurrency of Angle Bisectors By the Concurrency of Angle Bisectors of a Triangle Theorem, the incenterNis equidistant from the sides of ABC. So, to find ND, you can find NFin NAF. Use the Pythagorean Theorem. Pythagorean Theorem Substitute known values. Multiply. Subtract 256 from each side. Take the positive square root of each side. Because NF = ND, ND = 12.

  7. B P A B 4. Do you have enough information to conclude that QSbisects PQR? Explain. C P A C Practice In Exercises 1–3, find the value of x. P 1. 2. 3. B C 15 11 5 A 5. In diagram, suppose you are not given AF or AN, but you are given that BF = 12 and BN = 13. Find ND. 5

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