Using the State Curriculum: Mathematics, Grade 8Algebra  Geometry  Measurement  Statistics  Probability  Number  Processes 
Higher Order Thinking Skills: The higher order thinking skills shows examples of questions for this concept at various levels of cognitive demand. 
Standard 2.0 Knowledge of Geometry 
Topic D. Congruence and Similarity 
Indicator 1. Apply the properties of similar polygons 
Objective a. Determine similar parts of polygons 
Level 1: Knowledge/Comprehension 

The two quadrilaterals shown below are similar. Which side of quadrilateral WXYZ corresponds to ? Answer: The triangles below are similar. Which angle in corresponds to ? Answer: 
Level 2: Application/Analysis 
Figure GHIJK is similar to PQRST. If HG = 15 cm, what is the length of ? Answer: 10cm so that Look at the rectangles below. Is the 8 in by 10 in rectangle similar to the 3 in by 5 in rectangle? Justify your answer. Use words, numbers, and/or symbols in your justification. Sample correct response: No, the rectangles are not similar. The smaller sides of the rectangles are in the ratio of 3:8 but the larger sides are in the ratio of 5:10, or 1:2. Since the ratios of the sides are different, the rectangles are not similar. Look at the similar triangles below. What is the length, in centimeters, of the missing side? Answer: 30 cm Explain how you determined the length of the missing side. Use words, numbers, and/or symbols in your explanation. Sample correct response: Sample correct response: The length is 30 cm because the ratio 28:45, 30:45, and 40:60 all reduce to 2:3, which means all of the sides are in the same ratio. Since the figures are similar, the sides must all be in the same ratio. 
Level 3: Synthesis/Evaluation 
An 8" by 10" photograph will be surrounded by a 2" border as shown below. Will the framed photograph be similar to the 8" by 10" photograph? Justify your answer. Use words, numbers, and/or symbols in your justification. Sample correct response: No. The framed photograph will have dimensions 12" by 14". I found the new dimensions by adding the 2" border to the top and bottom and both sides. I checked to see if the sides were proportional. An 8" by 10" photograph will be surrounded by a border as shown below. The border on the width is 2". How wide should the border on the length be so that the framed photograph and the photograph are similar? Sample correct answer: The original length of the photograph is 10. To place a border on the length take the difference of 15 and 10 and split it in two. The border along the length should be 2.5". 
