5.3 use angle bisectors of triangles
- 1. 5.3 Use Angle Bisectors of Triangles 5.3 Bell Thinger 1. AD bisects ANSWER BAC. Find x. 20 2. Solve x² + 12² = 169. ANSWER ±5 3. The legs of a right triangle measure 15 feet and 20 feet. Find the length of the hypotenuse. ANSWER 25 ft
- 2. 5.3
- 3. Example 1 5.3 Find the measure of GFJ. SOLUTION Because JG FG and JH FH and JG = JH = 7, FJ bisects GFH by the Converse of the Angle Bisector Theorem. So, mGFJ = mHFJ = 42 .
- 4. Example 2 5.3 SOCCER A soccer goalie’s position relative to the ball and goalposts forms congruent angles, as shown. Will the goalie have to move farther to block a shot toward the right goalpost R or the left goalpost L?
- 5. Example 2 5.3 SOLUTION The congruent angles tell you that the goalie is on the bisector of LBR. By the Angle Bisector Theorem, the goalie is equidistant from BR and BL . So, the goalie must move the same distance to block either shot.
- 6. Example 3 5.3 ALGEBRA For what value of x does P lie on the bisector of A? SOLUTION From the Converse of the Angle Bisector Theorem, you know that P lies on the bisector of A if P is equidistant from the sides of A, so when BP = CP. BP = CP x + 3 = 2x –1 4=x Set segment lengths equal. Substitute expressions for segment lengths. Solve for x. Point P lies on the bisector of A when x = 4.
- 7. Guided Practice 5.3 In Exercises 1–3, find the value of x. 1. ANSWER 15
- 8. Guided Practice 5.3 In Exercises 1–3, find the value of x. 2. ANSWER 11
- 9. Guided Practice 5.3 In Exercises 1–3, find the value of x. 3. ANSWER 5
- 10. 5.3
- 11. 5.3
- 12. Example 4 5.3 In the diagram, N is the incenter of ABC. Find ND. SOLUTION By the Concurrency of Angle Bisectors of a Triangle Theorem, the incenter N is equidistant from the sides of ABC. So, to find ND, you can find NF in NAF. Use the Pythagorean Theorem stated on page 18.
- 13. Example 4 5.3 c 2 = a 2 + b2 2 2 20 = NF + 16 2 Pythagorean Theorem 2 400 = NF + 256 144 = NF 12 = NF 2 Substitute known values. Multiply. Subtract 256 from each side. Take the positive square root of each side. Because NF = ND, ND = 12.
- 14. Exit Slip 5.3 Find the value of x. 1. ANSWER 12
- 15. Exit Slip 5.3 Find the value of x. 2. ANSWER 20
- 16. Exit Slip 5.3 3. Point D is the incenter of XYZ. Find DB. ANSWER 10
- 17. 5.3 Homework Pg 327-330 #14, 19, 20, 24, 29