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Exploring Similar Figures in Geometry

Study properties, measurement, and relationships of points, angles, surfaces, and solids. Learn about similar figures with proportional sides and congruent angles. Practice finding missing lengths and solving proportions in similar shapes.

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Exploring Similar Figures in Geometry

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  1. Chapter 10 Geometry

  2. Do Now • Complete numbers 8 – 14 on page 430

  3. Chapter 10Lesson 6 Similar Figures Objective: Determine whether figures are similar and find a missing length in a pair of similar figures.

  4. Geometry The study of properties, measurement, and relationships of points, angles, surfaces and solids.

  5. Similar Figures Figures that have the same shape but not necessarily the same size. Corresponding sides are proportional Corresponding angles are congruent

  6. ~ = Congruent Equal

  7. A B AB EF D C E F Write each fraction in simplest form. 1. AB EF H G 31 9 3 = • BC • FG 1 3 =

  8. Indirect measurement Finding measurement by using similar triangles and writing a proportion

  9. A D F E C B ABC ~ DEF Corresponding sides: ABACBC DE DF EF = = ~ ~ = ~ Corresponding angles: A D; B E; C F = =

  10. A D 6 m 18 m 5 m 15 m B C E F 4 m If ABC ~ DEF, find the length of EF Write a proportion ACBC DF EF 64 18 n = N=12 =

  11. Kelly wants to resize a 4-inch wide by 5-inch long photo. It is to fit in a space that is 2 inches wide. What is the length of the resized photo in inches? X 5 in. 2 in. 4 in.

  12. Find the value of x in each pair of similar figures. A D 6 mi 30 mi 5 mi X B C E F

  13. Find the value of x in each pair of similar figures. A D 29.4 m 14 m B C E F 25.2 m X

  14. A B C D E F G H X 14 cm 9 cm 31.5 cm

  15. Determine whether each pair of figures is similar. Justify your answer. A B C D E F G H 6 in 18 in 33 in 11 in

  16. Determine whether each pair of figures is similar. Justify your answer. A D 21 km 54 km B E 18 km 63 km

  17. IfABC DEF, find the length of Example 6-1a

  18. Since the two triangles are similar, the ratios of their corresponding sides are equal. So, you can write and solve a proportion to find Let n represent the length of . Then substitute. Answer: The length of is 16.5 centimeters. Write a proportion. Find the cross products. Simplify. Divide each side by 3. Example 6-1a

  19. IfJKL MNO, find the length of Answer: 13.5 in. Example 6-1b

  20. GRID-IN TEST ITEMA rectangular picture window 12-feet long and 6-feet wide needs to be shortened to 9 feet in length to fit a redesigned wall. If the architect wants the new window to be similar to the old window, how wide will the new window be? Read the Test Item To find the width of the new window, draw a picture and write a proportion. Example 6-2a

  21. Solve the Test Item Write a proportion. Find the cross products. Divide each side by 12. Example 6-2a

  22. So, the width of the new window will be 4.5 feet. Answer: 4.5 feet Example 6-2a

  23. GRID-IN TEST ITEMTom has a rectangular garden which has a length of 12 feet and a width of 8 feet. He wishes to start a second garden which is similar to the first and will have a width of 6 feet. Find the length of the new garden. Answer: 9 Example 6-2b

  24. Kelly bought a miniature replica of the Statue of Liberty. The replica is 9 inches tall, and the length of the statue’s right arm holding the torch is 1 ¼ inches. • About how long is the State of Liberty’s right arm? • Kelly’s friend Bella brought home a smaller replica. The length of the Statue’s right arm is ¾ inch. How tall is Bella’s statue?

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