Parts of Similar Triangles Chapter 7-5 Parts of Similar Triangles

Five-Minute Check (over Lesson 7-4) Main Ideas California Standards Theorem 7.7: Proportional Perimeters Theorem Example 1: Perimeters of Similar Triangles Theorems: Special Segments of Similar Triangles Example 2: Write a Proof Example 3: Medians of Similar Triangles Example 4: Solve Problems with Similar Triangles Theorem 7.11: Angle Bisector Theorem Lesson 5 Menu

Standard 4.0 Students prove basic theorems involving congruence and similarity. (Key) Recognize and use proportional relationships of corresponding perimeters of similar triangles. Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles. Lesson 5 MI/Vocab

Proportionate Perimeters of Polygons (try saying that 10 times fast—quietly!!!) If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths. A B C D 6 12 9 15 W X Z Y 10 8 4 3 2

Perimeters of Similar Triangles Lesson 5 Ex1

Perimeters of Similar Triangles Proportional Perimeter Theorem Substitution. Cross products Multiply. Divide each side by 16. Lesson 5 Ex1

A. B. C. D. Lesson 5 CYP1

Similar Triangle Proportionality If two triangles are similar, then the ratio of any two corresponding lengths (sides, perimeters, altitudes, medians and angle bisector segments) is equal to the scale factor of the similar triangles.

Example Find the altitude QS. N M P Q R S T 24 6 16

A. B. C. D. Lesson 5 CYP2

Medians of Similar Triangles Lesson 5 Ex3

Medians of Similar Triangles Write a proportion. EG = 18, JL = x, EF = 36, and JK = 56 Cross products Divide each side by 36. Answer: Thus, JL = 28. Lesson 5 Ex3

A. 2.8 B. 17.5 C. 3.9 D. 0.96 A B C D Lesson 5 CYP3

Solve Problems with Similar Triangles Lesson 5 Ex4

Solve Problems with Similar Triangles Lesson 5 Ex4

Solve Problems with Similar Triangles Write a proportion. Cross products Simplify. Divide each side by 80. Answer: The height of the pole is 15 feet. Lesson 5 Ex4

A. 10.5 in B. 61.7 in C. 21 in D. 28 in Lesson 5 CYP4

Triangle Bisector Theorem If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. C A D B

Example #3 Find DC 14-x x 15 9 14 A B C D AD bisects BAC Triangle Bisector Thm. x

Homework Chapter 7-5 Pg 419 1-13 skip #3, 19-22, 25-26, 39-40