NAME _____________________________________________ DATE ____________________________ PERIOD _____________ 7-6 Study Guide and Intervention Parts of Similar Triangles Special Segments of Similar Triangles When two triangles are similar, corresponding altitudes, angle bisectors, and medians are proportional to the corresponding sides. Example: In the figure, ABC XYZ, with angle bisectors as shown. Find x. Since ABC XYZ, the measures of the angle bisectors are proportional to the measures of a pair of corresponding sides. = 24 10 = 8 10x = 24(8) 10x = 192 x = 19.2 Exercises Find x. 1. 2. 3. 4. 5. 6. Chapter 7 35 Glencoe Geometry NAME _____________________________________________ DATE ____________________________ PERIOD _____________ 7-6 Study Guide and Intervention (continued) Parts of Similar Triangles Triangle Angle Bisector Theorem An angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of the other two sides. Example: Find x. Since is an angle bisector, = . 20 15 = 30 30x = 20(15) 30x = 300 x = 10 Exercises Find the value of each variable. 1. 2. 3. 4. 5. 6. Chapter 7 36 Glencoe Geometry