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Lesson 5: Similar Figures — Practice Questions

  1. 1. If triangle LMN is similar to triangle RST, written as $\triangle LMN \sim \triangle RST$, which angle must be congruent to $\angle T$?

    • A. $\angle L$
    • B. $\angle M$
    • C. $\angle N$
    • D. $\angle R$
  2. 2. Given that quadrilateral $DEFG \sim MNOP$, the angle corresponding to $\angle F$ is $\angle$___.

  3. 3. Given that quadrilateral $ABCD \sim WXYZ$, which of the following ratios of side lengths must be correct?

    • A. $\frac{AB}{XY}$
    • B. $\frac{BC}{WZ}$
    • C. $\frac{CD}{YZ}$
    • D. $\frac{DA}{XY}$
  4. 4. If $\triangle PQR$ is similar to $\triangle STU$ such that P corresponds to S and Q corresponds to T, complete the similarity statement: $\triangle PQR \sim \triangle$___.

  5. 5. The statement $\triangle GHI \sim \triangle JKL$ implies that the ratio $\frac{GH}{JK}$ is equal to which other ratio?

    • A. $\frac{HI}{JL}$
    • B. $\frac{GI}{KL}$
    • C. $\frac{HI}{KL}$
    • D. $\frac{GH}{KL}$
  6. 6. Which statement best describes two similar figures?

    • A. Their corresponding angles are equal, and their corresponding sides are proportional.
    • B. Their corresponding sides are equal.
    • C. Their corresponding angles are equal, but their side lengths are not related.
    • D. They have the same area.
  7. 7. A rectangle has sides of 5 cm and 10 cm. A larger, similar rectangle has a shorter side of 15 cm. The length of its longer side is ___ cm.

  8. 8. A rectangle with sides 2 m and 5 m is compared to a rectangle with sides 6 m and 12 m. Are the two rectangles similar?

    • A. Yes, because their corresponding angles are all 90 degrees.
    • B. No, because the ratio of corresponding sides is not the same.
    • C. Yes, because one pair of sides is proportional.
    • D. No, because their areas are different.
  9. 9. A right triangle has legs of 5 ft and 12 ft. If it is enlarged by a scale factor of 3 to create a new similar triangle, the length of the shorter leg in the new triangle is ___ ft.

  10. 10. A map is reduced using a photocopier, creating a smaller, similar image. Which property of the original map is preserved in the smaller copy?

    • A. The side lengths
    • B. The area
    • C. The angle measures
    • D. The perimeter