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Parts of Similar Triangles

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

2 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

3 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

4 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

5 Perimeters of Similar Triangles
Lesson 5 Ex1

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

7 A. B. C. D. Lesson 5 CYP1

8 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.

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

10 A. B. C. D. Lesson 5 CYP2

11 Medians of Similar Triangles
Lesson 5 Ex3

12 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

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

14 Solve Problems with Similar Triangles
Lesson 5 Ex4

15 Solve Problems with Similar Triangles
Lesson 5 Ex4

16 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

17 A in B in C. 21 in D. 28 in Lesson 5 CYP4

18 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

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

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


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