Lesson 36: Writing and Solving Proportions — Practice Questions

1. 1. Two similar triangles have a scale factor of $\frac{2}{3}$. What is the ratio of their areas?

   • A. $\frac{2}{3}$
   • B. $\frac{4}{9}$
   • C. $\frac{8}{27}$
   • D. $\frac{4}{6}$

2. 2. The ratio of the volumes of two similar spheres is $1:64$. What is the ratio of their surface areas?

   • A. $1:4$
   • B. $1:8$
   • C. $1:16$
   • D. $1:64$

3. 3. Two similar prisms have heights of 4 cm and 6 cm. If the volume of the smaller prism is 80 cm$^3$, what is the volume of the larger prism in cm$^3$? ___

4. 4. Two similar pentagons have a side length ratio of $5:3$. What is the ratio of their perimeters?

   • A. $5:3$
   • B. $25:9$
   • C. $125:27$
   • D. $10:6$

5. 5. Two similar rectangular posters have a scale factor of $\frac{3}{5}$. The area of the larger poster is 75 square feet. What is the area of the smaller poster in square feet? ___

6. 6. Given that $\triangle ABC \sim \triangle XYZ$. If $AB = 6$, $BC = 10$, and the corresponding side $XY = 9$, what is the length of side $YZ$? The length of $YZ$ is ___.

7. 7. Which of the following statements must be true for two polygons to be considered similar?

   • A. Their corresponding angles must be congruent, and their corresponding sides must be congruent.
   • B. Their corresponding angles must be congruent, and the ratio of their corresponding side lengths must be equal.
   • C. They must have the same number of sides and the same area.
   • D. Their corresponding sides must have an equal ratio, but their angles can be different.

8. 8. Suppose $\triangle DEF \sim \triangle GHI$. If $m\angle D = 55^\circ$ and $m\angle H = 95^\circ$, what is the measure of $\angle F$?

   • A. 30°
   • B. 55°
   • C. 95°
   • D. 150°

9. 9. Rectangle $PQRS$ is similar to rectangle $WXYZ$. Side $PQ=18$ and its corresponding side $WX=12$. What is the ratio of the side lengths of rectangle $WXYZ$ to rectangle $PQRS$? Express your answer as a fraction in simplest form: ___.

10. 10. Quadrilateral $GHIJ$ is similar to quadrilateral $KLMN$. Given $GH = 20$, $HI = 24$, and the corresponding side $KL = 15$. What is the length of side $LM$?

    • A. 16
    • B. 18
    • C. 19
    • D. 32