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Geometry Proportional Perimeters & Similar Triangles Explanation

Learn how to use ratios to find the perimeters of similar triangles and apply the Triangle Angle Bisector Theorem in this detailed geometry review. Practice solving various examples to enhance your understanding. Master the concepts with this comprehensive quiz.

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Geometry Proportional Perimeters & Similar Triangles Explanation

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  1. Review Quiz: 1. Maria is 4 ft 2 in. tall. To find the height of a flagpole, she measured her shadow and the pole’s shadow. What is the height h of the flagpole? 2. A blueprint for Latisha’s bedroom uses a scale of 1 in.:4 ft. Her bedroom on the blueprint is 3 in. long. How long is the actual room? 25 ft 12 ft

  2. Parts of Similar Triangles Section 6-5

  3. Proportional Perimeters Theorem • If 2 triangles are similar, then the perimeters are proportional to the measures of the corresponding sides.

  4. The similarity ratio of ∆LMN to ∆QRS is Example: Using Ratios to Find Perimeters Given that ∆LMN~∆QRS, find the perimeter P of ∆QRS. So the ratio of the perimeters is also 13/9.1. The perimeter of ∆QRS is 25.2 cm. 13P = 36(9.1) P = 25.2

  5. Example: ∆ABC ~ ∆DEF, BC = 4 mm, and EF = 12 mm. If P = 42 mm for ∆DEF, find the perimeter of ∆ABC. 12P = 42(4) P = 14 mm The perimeter of ∆ABC is 14 mm.

  6. Example: Using the Triangle Angle Bisector Theorem Find PS and SR. x = 30

  7. Example: Find AC and DC. y = 18 So DC = 9 and AC = 16.

  8. Lesson Quiz: Part I Find the length of each segment. 1.2. SR = 25, ST = 15

  9. Lesson Quiz: Part II 3. ∆ABC ~ ∆DEF. Find the perimeter of ∆ABC. P = 27 in.

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