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TIgeometry.com Geometry Angle Bisectors in a Triangle Name ___________________________ ID: 8892 Class ___________________________ In this activity, you will explore: The angle bisector of an angle. The proportional relationship that occurs when an angle bisector in a triangle divides the opposite side into two parts. Use this document to record your answers. Problem 1 – The Angle Bisector Theorem 1. What were the measures of the two angles created by your angle bisector (BAX and CAX)? 2. Record some of the measurements after moving point X: Distance from X to side AB Distance from X to side AC 3. Complete the conjecture: Any point on the angle bisector of an angle is _______________ from the sides of the angle. Problem 2 – One Angle Bisector in a Triangle 4. Record some of the measurements after moving a vertex of ABC: AB ©2007 Texas Instruments Incorporated AC BD Page 1 CD Angle Bisectors in a Triangle TIgeometry.com Geometry 5. Identify a pair of ratios that are equal. Drag a vertex of the triangle to confirm your conjecture. _______ = _______ Apply The Math Use your proportion from question 5 above to find the missing values for each: 6. 7. 4.5 3 2 30 ? 15 ? 18 8. Create your own problem and solve it below. ©2007 Texas Instruments Incorporated Page 2 Angle Bisectors in a Triangle