Question: Example 2 Using Angle Bisectors In the diagram, the angle bisectors of A JKL meet at point H. a. What segments are congruent? b. Find

Example 2 Using Angle Bisectors In the diagram, the angle bisectors of A JKL meet at point H. a. What segments are congruent? b. Find HN and HP. Solution 24 a. By Theorem 5.6, the three angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle. So, HM = HN = HP. Therefore, HM, HN, and HP are congruent b. Use the Pythagorean Theorem to find HN in AHNK. (HN)2 + 1 1= = 1 $2 Pythagorean Theorem (HN) 2 + 2 = Substitute. (HN) 2 + Evaluate each square. (NN)2 = Subtract from each side HN Find the positive square root. Answer So, HN = HP = units. Checkpoint Complete the following exercise. 2. The angle bisectors of &TUV meet at point W. Find the value of d. 2d+7 x way V 4d-1

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