Similar Figures Examples and Step by Step Directions

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.

Example  Are these 2 figures similar?

 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.

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.

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

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

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

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.

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.

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/ 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/ x 1/9 = 20 cm 2