Click the mouse button or press the Space Bar to display the answers. Objective Determine whether figures are similar and find a missing length in a pair of similar figures Vocabulary Similar Figures Figures that have the same shape but not necessarily the same size Vocabulary Indirect measurement Finding a measurement by using similar triangles and writing a proportion Vocabulary Proportion An equation that shows that two ratios are equivalent Math Symbols Is similar to Example 1 Find Side Measures of Similar Triangles Example 2 Use Indirect Measurement If ABC DEF, find the length of Small Large = Triangles are similar so start with a proportion To set up determine what you are working with Small triangle and a large triangle 1/2 If ABC DEF, find the length of Small 3 = Large 4.5 Find a side on each triangle that is similar On the first ratio, put 3 with the small triangle On the first ratio, put 4.5 with the large triangle 1/2 If ABC DEF, find the length of Small 3 = x Large 4.5 Define the variable Since DF is on the large triangle, place the variable in the denominator Find the side similar to DF on the small triangle 1/2 If ABC DEF, find the length of Small 3 11 = x Large 4.5 Since 11 is with the small triangle, place 11 in the numerator Solve for x by using cross multiplication 1/2 If ABC DEF, find the length of Small 3 11 = x Large 4.5 3x = 4.5(11) 3x = 49.5 3 3 Cross multiply Combine “like” terms Ask “What is being done to the variable?” The variable is being multiplied by 3 Do the inverse on both sides of the equal sign Using a fraction bar, divide both sides by 3 1/2 If ABC DEF, find the length of Small 3 11 = x Large 4.5 3x = 4.5(11) 3x = 49.5 3 3 1 x = 16.5 x = 16.5 Combine “like” terms Use the Identity Property to multiply 1 x The question asked to find the length of DF Add dimensional analysis Answer: DF = 16.5 cm 1/2 If JKL MNO, find the length of Answer: JL = 13.5 in 1/2 A 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? 6 ft 12 ft Small Large = x ft 9 ft Draw a picture of the two windows and put in the dimensions Set up the proportion Make the first ratio with similar sides from each window 2/2 A 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? 6 ft 12 ft Small 9 = Large 12 x x ft 9 ft The small window length is 9 ft The large window length is 12 ft Define the variable The new window is the small window 2/2 A 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? 6 ft 12 ft Small 9 = Large 12 x 6 x ft 9 ft The similar wide is the width of the large window Find the value of x by cross multiplying 2/2 A 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? Cross multiply Small 9 = x 6 Large 12 Combine “like” terms 12x = 9(6) 12x = 54 12 12 Ask “What is being done to the variable?” The variable is being multiplied by 12 Do the inverse on both sides of the equal sign Using a fraction bar, divide both sides by 12 2/2 A 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? Combine “like” terms Small 9 = x 6 Large 12 Use the Identity Property to multiply 1 x 12x = 9(6) Add dimensional analysis 12x = 54 12 12 1 x = 4.5 Answer: x = 4.5 ft 2/2 * Tom 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. Draw the gardens and label dimensions Answer: x = 9 ft 2/2 Assignment Lesson 10:6 Similar Figures 3 - 12 All