# Using the State Curriculum: Mathematics, Grade 8

 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 ?

The triangles below are similar.

Which angle in corresponds to ?

### Level 2: Application/Analysis

Figure GHIJK is similar to PQRST.

If HG = 15 cm, what is the length of ?

so that

Look at the rectangles below.

Is the 8 in by 10 in rectangle similar to the 3 in by 5 in rectangle?

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?

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?