ACT Math : How to find if quadrilaterals are similar

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find If Quadrilaterals Are Similar

The sides of rectangle A measure to , and . Rectangle B is similar to Rectangle A. The shorter sides of rectangle B measure  each. How long are the longer sides of Rectangle B?

Possible Answers:

Correct answer:

Explanation:

In similar rectangles, the ratio of the sides must be equal.

To solve this question, the following equation must be set up:

, using  as the variable for the missing side. 

We then must cross multiply, which leaves us with:

Lastly, we divide both sides by 8 to solve for the missing side:

Therefore, the longer sides of the rectangle are each .

Example Question #2 : How To Find If Quadrilaterals Are Similar

Suppose a rectangle has side lengths of 7 and 3.  Another rectangle has another set of side lengths that are 8 and 4.  Are these similar rectangles, and why?

Possible Answers:

Correct answer:

Explanation:

Set up the proportion to determine if the ratios of both rectangles are equal.  

If they are, then they are similar.  

These are not similar rectangles since their ratios are not the same.

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