Connecting Similarity and Transformations

ID: hilik-masot
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Connecting Similarity and Transformations

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Problem 1

1) Find a sequence of rigid motions and dilations that takes square ABCDABCD to square EFGHEFGH.

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Problem 2

Quadrilaterals QQ and PP are similar.

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2) What is the scale factor of the dilation that takes PP to QQ?

3) What is the scale factor of the dilation that takes QQ to PP?

Problem 3

4) What is our definition of similarity?

a) If 2 figures have the same angles, then they are similar.\text{If 2 figures have the same angles, then they are similar.}b) If 2 figures have proportional side lengths, then they are similar.\text{If 2 figures have proportional side lengths, then they are similar.}c) If there is a sequence of rigid transformations taking one figure to another, then they are similar.\text{If there is a sequence of rigid transformations taking one figure to another, then they are similar.}d) If there is a sequence of rigid transformations and dilations that take one figure to the other, then they are similar.\text{If there is a sequence of rigid transformations and dilations that take one figure to the other, then they are similar.}
Problem 4

5) Triangle DEFDEF is formed by connecting the midpoints of the sides of triangle ABCABC. The lengths of the sides of DEFDEF are shown. What is the length of BCBC?

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a) 3 units\text{3 units}b) 4 units\text{4 units}c) 6 units\text{6 units}d) 8 units\text{8 units}
Problem 5

6) If ABAB is 12, what is the length of ABA'B'?

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Problem 6

7) Right angle ABCABC is taken by a dilation with center PP and scale factor 12\frac{1}{2} to angle ABCA'B'C'. What is the measure of angle ABCA'B'C'?

Problem 7

8) Dilate point CC using center DD and scale factor 34\frac{3}{4}.

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9) Dilate segment ABAB using center DD and scale factor 12\frac{1}{2}.

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Problem 8

10) A polygon has perimeter 12. It is dilated with a scale factor of kk and the resulting image has a perimeter of 8. What is the scale factor?

a) 12 \frac{1}{2} b) 23 \frac{2}{3} c) 34 \frac{3}{4} d) 43 \frac{4}{3}
Problem 9

11) Select all the statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.

a) Parallelograms have four congruent sides. \quad\quad b) Both sets of opposite sides of a parallelogram are parallel and congruent. c) A trapezoid is a parallelogram. \quad\quad d) Diagonals of a parallelogram bisect each other. \quad\quad e) Diagonals of a parallelogram are congruent.