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Finding Unknown Lengths in Similar Figures

Learn how to use similar figures to find unknown lengths using proportions. Watch a video on similar figures and practice solving examples.

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Finding Unknown Lengths in Similar Figures

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  1. JN KO Warm Up Solve each proportion. 24 x 6 19 k 4 75 25 x = 76 k = 12 2. 1. = = Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles. 3. A J Z O K N

  2. Learn to use similar figures to find unknown lengths. Similar Figures Video

  3. Indirect measurementis a method of using proportions to find an unknown length or distance in similar figures. http://youtu.be/J7gyN2M8PhA

  4. Additional Example 1: Finding Unknown Lengths in Similar Figures Find the unknown measures in the similar figures. H B A 31° 10 cm y 5.8 cm x 6 cm 116 cm 59° J G 5 cm C AB JG BC HG = Write a proportion using corresponding sides. 6 x 10 5 = Substitute lengths of the sides. 10 · x= 5 · 6 Find the cross product. Multiply. 10x = 30 30 10 10x 10 = Divide each side by 12 to isolate the variable. x = 3 HG is 3 centimeters.

  5. Additional Example 1 Continued Find the unknown measures in the similar figures. H B A 31° 10 cm y 5.8 cm x 6 cm 116 cm 59° J G 5 cm C Step 2 Find y. Corresponding angles of similar triangles have equal angle measures. H corresponds to C y = 59

  6. Check It Out: Example 1 Find the unknown measures in the similar figures. D B A 27° 14 cm y 5.8 cm x 9 cm 116 cm 63° F E 7 cm C AB FE BC DE = Write a proportion using corresponding sides. 9 x 14 7 = Substitute lengths of the sides. 14 · x= 9 · 7 Find the cross product. Multiply. 14x = 63 63 14 14x 14 = Divide each side by 12 to isolate the variable. x = 4.5 HG is 4.5 centimeters.

  7. Check It Out: Example 1 Continued Find the unknown measures in the similar figures. D B A 27° 10 cm y 5.8 cm x 6 cm 116 cm 63° F E 5 cm C Step 2 Find y. Corresponding angles of similar triangles have equal angle measures. D corresponds to C y = 63

  8. Additional Example 2: Measurement Application The inside triangle is similar in shape to the outside triangle. Find the length of the base of the inside triangle. Let x = the base of the inside triangle. 8 2 12 x Write a proportion using corresponding side lengths. = 8 · x = 2 · 12 Find the cross products. Multiply. 8x = 24 8x 8 24 8 = Divide each side by 8 to isolate the variable. x = 3 The base of the inside triangle is 3 inches.

  9. Additional Example 3: Estimating with Indirect Measurement City officials want to know the height of a traffic light. Estimate the height of the traffic light. 48.75 h 27.25 15 = Write a proportion. 25 15 Use compatible numbers to estimate. 50 h ≈ h ft 5 3 50 h Simplify. ≈ 27.25 ft Cross multiply. 5h ≈ 150 48.75 ft Divide each side by 5 to isolate the variable. h ≈ 30 The traffic light is about 30 feet tall.

  10. Check It Out: Example 3 The inside triangle is similar in shape to the outside triangle. Find the height of the outside triangle. h 30.25 5 14.75 = Write a proportion. Use compatible numbers to estimate. 5 15 h 30 ≈ h ft 5 ft 13 h 30 ≈ Simplify. Cross multiply. 1 • 30≈ 3• h 14.75 ft Divide each side by 3 to isolate the variable. 30≈ 3h 30.25 ft 10≈ h The outside triangle is about 10 feet tall.

  11. Homework Workbook Pg. 203

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