School Improvement in Maryland

Using the State Curriculum: Mathematics, Grade 8

Algebra | 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.

two quadrilaterals

Which side of quadrilateral WXYZ corresponds to DE?

Answer: WZ

The triangles below are similar.

two triangles

Which angle in triangle RST corresponds to angle MNP?

Answer: angle RST

Level 2: Application/Analysis

Figure GHIJK is similar to PQRST.

geometric images

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

Answer: 10cm

24/16=15x

so that equation image

equations image

Look at the rectangles below.

rectangles

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.

triangle

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:

equations image

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.

photo

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.

equation image

An 8" by 10" photograph will be surrounded by a border as shown below. The border on the width is 2".

photo

How wide should the border on the length be so that the framed photograph and the photograph are similar?

Sample correct answer:

equations image

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".

/toolkit/vsc/thinking_skills/mathematics/grade8/2D1a.xml
Resources for Objective 2.D.1.a:
THINKING SKILLS | Sample Assessments |