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Lesson 9-4: Similarity and Corresponding Parts — 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. In $\Delta LMN$, $m\angle L = 52^\circ$ and $m\angle M = 78^\circ$. In $\Delta PQR$, $m\angle P = 52^\circ$ and $m\angle Q = 78^\circ$. Are the two triangles similar?

    • A. Yes, by the AA Similarity Criterion.
    • B. No, the third angles might be different.
    • C. No, side lengths are needed to determine similarity.
    • D. Yes, because all triangles are similar.
  7. 7. In $\Delta ABC$, $m\angle A = 65^\circ$ and $m\angle B = 40^\circ$. In $\Delta XYZ$, $m\angle X = 65^\circ$ and $m\angle Z = 75^\circ$. To check for similarity, first find the measure of $\angle C$ in degrees. $m\angle C = $ ___.

  8. 8. Triangle $RST$ has angles measuring $30^\circ$ and $90^\circ$. Which of the following triangles is similar to $\Delta RST$?

    • A. A triangle with angles $30^\circ$ and $80^\circ$
    • B. A triangle with angles $90^\circ$ and $50^\circ$
    • C. A triangle with angles $30^\circ$ and $60^\circ$
    • D. A triangle with angles $90^\circ$ and $30^\circ$
  9. 9. Triangle $GHI$ is similar to $\Delta JKL$. If $m\angle G = 25^\circ$ and $m\angle I = 110^\circ$, and $m\angle J = 25^\circ$, what is the measure of $\angle K$ in degrees? $m\angle K = $ ___.

  10. 10. Which condition is sufficient to prove that two triangles are similar by the Angle-Angle (AA) Similarity Criterion?

    • A. One pair of corresponding angles is congruent.
    • B. Two pairs of corresponding angles are congruent.
    • C. One pair of corresponding sides is congruent.
    • D. Two pairs of corresponding sides are proportional.