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Similar Figures Examples and Step by Step Directions.

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Presentation on theme: "Similar Figures Examples and Step by Step Directions."— Presentation transcript:

1 Similar Figures Examples and Step by Step Directions

2 Are Two Figures Similar?  Step1: Set up all corresponding sides into ratios(fractions).  Step2: Reduce all ratios.  Step3: If all ratios reduce to the same fraction, then the two figures are similar. If all ratios do not reduce to the same fraction, then the two figures are not similar.  Step1: Set up all corresponding sides into ratios(fractions).  Step2: Reduce all ratios.  Step3: If all ratios reduce to the same fraction, then the two figures are similar. If all ratios do not reduce to the same fraction, then the two figures are not similar.

3 Example  Are these 2 figures similar?

4  3/6 = 1/2  4/8 = 1/2  5/10 = 1/2  Yes, they are similar because all 3 sets of ratios of corresponding sides reduce to the same fraction.  3/6 = 1/2  4/8 = 1/2  5/10 = 1/2  Yes, they are similar because all 3 sets of ratios of corresponding sides reduce to the same fraction.

5 Finding A Missing Side Length in Similar Figures  Step 1: Set up one set of corresponding sides into a ratio and reduce.  Step 2: That reduced ratio is the scale factor. Set that scale factor = to the ratio of corresponding sides where you don’t know the measure of one side. Cross multiply and divide to solve for x.  Step 1: Set up one set of corresponding sides into a ratio and reduce.  Step 2: That reduced ratio is the scale factor. Set that scale factor = to the ratio of corresponding sides where you don’t know the measure of one side. Cross multiply and divide to solve for x.

6 Example  Triangle GJH ~ Triangle TRS. Find the missing side length, x.

7  Step 1:  Step 2: 2x = 18 x = 9  Step 1:  Step 2: 2x = 18 x = 9

8 Finding Area of Similar Figures  Step 1: Find the scale factor, represented by a lower case r. Give both smaller and larger scale factors. Ex. 2/1 and 1/2  Step 2: Square the scale factor to find the relationship between the areas. If the scale factor is a ratio, square both numerator and denominator. Give both the larger and smaller r 2. Ex. 4/1 and 1/4  Step 1: Find the scale factor, represented by a lower case r. Give both smaller and larger scale factors. Ex. 2/1 and 1/2  Step 2: Square the scale factor to find the relationship between the areas. If the scale factor is a ratio, square both numerator and denominator. Give both the larger and smaller r 2. Ex. 4/1 and 1/4

9 Finding Area of Similar Figures Continued.  Step 3: Find the area of one of the figures that you have been given enough information to find. You will either be given the L and W of a rectangle or the problem will tell you one of the areas.

10 Finding Area of Similar Figures Continued  Step 4: Find the area of the other figure. *If you are looking for the area of the larger figure, then multiply area of smaller figure by larger r 2. *If you are looking for the area of the smaller figure, then multiply area of larger figure by smaller r 2.  Step 4: Find the area of the other figure. *If you are looking for the area of the larger figure, then multiply area of smaller figure by larger r 2. *If you are looking for the area of the smaller figure, then multiply area of larger figure by smaller r 2.

11 Area of Similar Figures Example  Rectangle ABCD ~ Rectangle QRST. BC = 4 cm and RS = 12 cm. The area of QRST is 180 cm 2. What is the area of ABCD? Step 1: Find r. r = 4/12 = 1/3 or 3/1 Step 2. Find r 2. r 2 = (1/3) 2 = 1/9 or 9/1 Step 3: Find area of QRST. 180 cm 2 Step 4: Multiply larger area in step 3 by smaller r 2, which is 1/9. 180 x 1/9 = 20 cm 2  Rectangle ABCD ~ Rectangle QRST. BC = 4 cm and RS = 12 cm. The area of QRST is 180 cm 2. What is the area of ABCD? Step 1: Find r. r = 4/12 = 1/3 or 3/1 Step 2. Find r 2. r 2 = (1/3) 2 = 1/9 or 9/1 Step 3: Find area of QRST. 180 cm 2 Step 4: Multiply larger area in step 3 by smaller r 2, which is 1/9. 180 x 1/9 = 20 cm 2


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