Parts of Similar Triangles

2. Parts of Similar Triangles Sec: 6.5 Sol:

3. Proportional Perimeters • If two triangles are similar, then the _____________ are proportional to the measures of corresponding sides. Remember: The perimeter is the sum of all the ______________ of a figure. Perimeters Sides Example:In the figure at the right, ABC ~ XYZ.The following proportions are true:

4. Example • In the figure below, ABD ~ ADC.If AD = 16, AC = 31, and DC = 23, find theperimeter of ABD.

5. Theorem 6.8 If two triangles are similar, then the measures of the corresponding ______________ are proportional to the measures of the corresponding sides. Remember: The _________________ is a segment that goes from a vertex and is perpendicular to the opposite “side”. Altitudes Altitude

6. Theorem 6.9 • If two triangles are similar, then the measures or lengths of the corresponding ___________ __________ of the triangles are proportional to the measures of the corresponding sides. • Example:TSR ~ GFE. is an angle bisector of RTS.is an angle bisector of EGF.List some possible proportions: Angle Bisectors

7. Theorem 6.10 • If two triangles are similar, then the measures of the corresponding ________ are proportional to the measures of the corresponding sides. • Remember: A _______ goes from a vertex to the ________ of the opposite side. • Example:CAB ~ YWX. is median of CAB.is median of YWX.List some possible proportions: Medians Median Middle

8. Angle Bisector Theorem: • An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other two sides. • Example:is the angle bisector of ACB.Complete the following statement:

9. J E K I C D Example: • In the figure is and altitude of and is an altitude of . Find x if . L G

10. Example: • The Drawing represents two poles supported by wires. . Find the height of pole . B E 30FT A F G C D 80FT

11. Suggested Assignments: • Classwork: • Homework: pg 10-14e, 17, 22-26e, 28