5-8 Using Similar Figures Do Now Test Friday on chapter5 section 1-8 Course 2 5-8 Using Similar Figures Do Now Test Friday on chapter5 section 1-8 Solve each proportion. k 4 75 25 6 19 24 x 1. = k = 12 2. x = 76 = Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles. 3. J A N Z K O JN KO

5-8 Using Similar Figures Course 2 5-8 Using Similar Figures EQ: How do I use similar figures to find unknown lengths? M7G3.a Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding parts; M7G3.b Understand the relationships among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length ratios, and area ratios to determine side lengths and areas of similar geometric figures

Open Textbook to page 302-303, work quietly on #1-8 and 13-15 On #1-8, I need your corresponding sides and angles along with the ratios!

Insert Lesson Title Here Course 2 5-8 Using Similar Figures Insert Lesson Title Here Vocabulary indirect measurement

5-8 Using Similar Figures Course 2 5-8 Using Similar Figures Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.

Additional Example 1: Determining Whether Two Triangles Are Similar Course 2 5-7 Similar Figures and Proportions Additional Example 1: Determining Whether Two Triangles Are Similar Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar. E AB corresponds to DE. 16 in 10 in A C 28 in BC corresponds to EF. 4 in D 7 in 40 in F AC corresponds to DF. B AB DE = ? BC EF = ? AC DF Write ratios using the corresponding sides. 4 16 = ? 7 28 = ? 10 40 Substitute the length of the sides. 1 4 = ? 1 4 = ? 1 4 Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the triangles are similar.

Additional Example 1: Determining Whether Two Triangles Are Similar Course 2 5-7 Similar Figures and Proportions Additional Example 1: Determining Whether Two Triangles Are Similar Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar. E AB corresponds to DE. 15 in X in A C 30 in BC corresponds to EF. 3 in D 6 in 40 in F AC corresponds to DF. B AB DE = BC EF = AC DF

Additional Example 1: Finding Unknown Lengths in Similar Figures Course 2 5-8 Using Similar Figures Additional Example 1: Finding Unknown Lengths in Similar Figures Find the unknown length in similar figures. AC QS = AB QR Write a proportion using corresponding sides. 12 48 14 w = Substitute lengths of the sides. 12 · w = 48 · 14 Find the cross product. 12w = 672 Multiply. 12w 12 672 12 = Divide each side by 12 to isolate the variable. w = 56 QR is 56 centimeters.

Insert Lesson Title Here Course 2 5-8 Using Similar Figures Insert Lesson Title Here Check It Out: Example 1 Find the unknown length in similar figures. x 10 cm Q R A B 12 cm 24 cm D C S T AC QS AB QR = Write a proportion using corresponding sides. 12 24 10 x = Substitute lengths of the sides. 12 · x = 24 · 10 Find the cross product. 12x = 240 Multiply. 12x 12 240 12 = Divide each side by 12 to isolate the variable. x = 20 QR is 20 centimeters.

Insert Lesson Title Here Course 2 5-8 Using Similar Figures Insert Lesson Title Here 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. 8x = 24 Multiply. 8x 8 24 8 = Divide each side by 8 to isolate the variable. x = 3 The base of the inside triangle is 3 inches.

Insert Lesson Title Here Course 2 5-8 Using Similar Figures Insert Lesson Title Here Check It Out: Example 2 The rectangle on the left is similar in shape to the rectangle on the right. Find the width of the right rectangle. 12 cm 6 cm 3 cm ? Let w = the width of the right rectangle. 6 12 3 w Write a proportion using corresponding side lengths. = 6 ·w = 12 · 3 Find the cross products. 6w = 36 Multiply. 6w 6 = 36 6 Divide each side by 6 to isolate the variable. w = 6 The right rectangle is 6 cm wide.

Additional Example 3: Estimating with Indirect Measurement Course 2 5-8 Using Similar Figures 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. 27.25 15 48.75 h = Write a proportion. 27 15 49 h Use compatible numbers to estimate. h ft ≈ 9 5 49 h ≈ Simplify. 27.25 ft 9h ≈ 245 Cross multiply. 48.75 ft h ≈ 27 Multiply each side by 9 to isolate the variable. The traffic light is about 30 feet tall.

5-8 Using Similar Figures Check It Out: Example 3 Course 2 5-8 Using Similar Figures Check It Out: Example 3 The inside triangle is similar in shape to the outside triangle. Find the height of the outside triangle. 5 14.75 h 30.25 = Write a proportion. 5 15 h 30 Use compatible numbers to estimate. ≈ h ft 5 ft 13 h 30 ≈ Simplify. 1 • 30 ≈ 3 • h Cross multiply. 14.75 ft 30 ≈ 3h Multiply each side by 5 to isolate the variable. 30.25 ft 10 ≈ h The outside triangle is about 10 feet tall.

Additional Example 1: Geography Application Triangles ABC and EFG are similar. Find the length of side EG. F E G 9 ft x B A C 3 ft 4 ft Triangles ABC and EFG are similar. The length of side EG is 12 ft.

Triangles DEF and GHI are similar. Find the length of side HI. Check It Out: Example 1 Triangles DEF and GHI are similar. Find the length of side HI. H G I 8 in x E D F 7 in 2 in Triangles DEF and GHI are similar. The length of side HI is 28 in.

A 30-ft building casts a shadow that is 75 ft long A 30-ft building casts a shadow that is 75 ft long. A nearby tree casts a shadow that is 35 ft long. How tall is the tree?

1. Vilma wants to know how wide the river near her house is 1. Vilma wants to know how wide the river near her house is. She drew a diagram and labeled it with her measurements. How wide is the river? 2. A yardstick casts a 2-ft shadow. At the same time, a tree casts a shadow that is 6 ft long. How tall is the tree? 7.98 m w 7 m 5 m 5.7 m 9 ft

Insert Lesson Title Here Course 2 5-8 Using Similar Figures Insert Lesson Title Here TOTD Find the unknown length in each pair of similar figures. 1. x = 120 cm 2. t = 150 cm

Insert Lesson Title Here Course 2 5-8 Using Similar Figures Insert Lesson Title Here TOTD Find the unknown length in each pair of similar figures. 3. The width of the smaller rectangular cake is 5.75 in. The width of a larger rectangular cake is 9.25 in. Estimate the length of the larger rectangular cake. x = 15 inches