Dilating Lines and Angles

ID: kuhuf-visat
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Dilating Lines and Angles

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Problem 1

1) Angle ABCABC is taken by dilation with center PP and scale factor 3 to angle ABCA'B'C'. The measure of angle ABCABC is 21°21\degree. What is the measure of angle ABCA'B'C'?

Problem 2

2) Select all lines that could be the image of line mm by a dilation. Write each corresponding letter in the answer box and separate letters with commas.


a) ll \quad\quad b) mm \quad\quad c) nn \quad\quad d) oo \quad\quad e) pp

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Problem 3

3) Dilate line ff with a scale factor of 2. The image is line gg. Which labeled point could be the center of this dilation?

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a) A A b) B B c) C C d) D D
Problem 4

4) Quadrilateral ABCEA'B'C'E' is the image of quadrilateral ABCEABCE after a dilation centered at FF. What is the scale factor of this dilation?

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Problem 5

5) A polygon has a perimeter of 18 units. It is dilated with a scale factor of 32\frac{3}{2}. What is the perimeter of its image?

a) 12 units\text{12 units}b) 24 units\text{24 units}c) 27 units\text{27 units}d) 30 units\text{30 units}
Problem 6

6) Solve the equation.

47=10x\frac{4}{7} = \frac{10}{x}

Problem 7

7) Here are some measurements for triangle ABCABC and triangle XYZXYZ:

  \bullet \ \  Angle CABCAB and angle ZXYZXY are both 30 degrees

  AC\bullet \ \ AC and XZXZ both measure 3 units

  CB\bullet \ \ CB and ZYZY both measure 2 units

Andre thinks thinks these triangles must be congruent. Clare says she knows they might not be congruent. Construct 2 triangles with the given measurements that aren't congruent. Explain why triangles with 3 congruent parts aren't necessarily congruent.