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Exploring Proportionality Relationships in Geometry

Discover the similarities, solve proportions, find ratios, and explore observations in similar triangles. Solve problems involving perimeters, areas, and side lengths in proportionate shapes. Enhance your geometry skills with practical exercises.

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Exploring Proportionality Relationships in Geometry

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  1. 7.5 Using Proportionality Relationships • Warm-up 20 24 8 x 30 19 36 x

  2. Lets Get Started! • How are these ’s similar? • Write a similarity statement. • C. Write the proportions and solve for x.

  3. M Let’s Explore! A 16 • ABC ~ MNO • Find x • Find the similarity ratio of ABC : MNO • Complete the ratio  • Observations? 8 O B C N 3 x

  4. Let’s Explore! M P • ABCD ~ MNOP • Find x • Find the similarity ratio of ABCD : MNOP • Complete the ratio  • Observations? A D x 3 B C N O 6 9

  5. M Let’s Explore! A 12 • ABC ~ MNO • Find the similarity ratio of ABC : MNO • Complete the ratio  • Observations? 9 h =6 h = 8 O B C N 12 16

  6. Let’s Explore! M P • ABCD ~ MNOP • Find the similarity ratio of ABCD : MNOP • Complete the ratio  • Observations? A D ½ 1 ½ B C N O ¼ ¾

  7. Solve: • Two similar triangles have side length in a ratio of 3ft:4ft. The perimeter of the smallest triangle is 96. Find the perimeter of the biggest triangle. • Two rhombii have areas in the ratio of 121in2: 196in2 • what is the ratio of their perimeters? • what is the ratio of their side lengths?

  8. Solve: • If the ratio of the perimeters of two pentagons is • 5: 8 and the area of the smaller pentagon is 75cm2, • what is the area of the larger pentagon?

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