Congruence and similarity Knowledge-Based Practice

Questions

1. 1.

   In $\triangle ABC$ and $\triangle DEF$, the side lengths are given as $AB = 6$, $BC = 8$, $DE = 9$, and $EF = 12$. Which additional condition is sufficient to prove that $\triangle ABC \sim \triangle DEF$ by the Side-Angle-Side (SAS) similarity criterion?

   • A) $\angle B \cong \angle E$
   • B) $\angle A \cong \angle D$
   • C) $\angle C \cong \angle F$
   • D) $\angle B \cong \angle D$
2. 2.

   Quadrilateral ABCD is similar to quadrilateral EFGH. If the perimeter of ABCD is 45 cm, the perimeter of EFGH is 60 cm, and the length of side CD is 12 cm, what is the length of the corresponding side GH?

   • A) 15 cm
   • B) 16 cm
   • C) 18 cm
   • D) 20 cm
3. 3.

   Given that $\triangle KLM \sim \triangle RST$, the measure of angle $K$ is $48^\circ$, and the measure of angle $T$ is $67^\circ$. What is the measure of angle $L$?

   • A) $48^\circ$
   • B) $55^\circ$
   • C) $65^\circ$
   • D) $67^\circ$
4. 4.

   Given that $\triangle ABC \cong \triangle PQR$, where $AB = 4x - 5$, $PQ = x + 16$, and $BC = 3x - 2$, what is the length of side $QR$?

   • A) 7
   • B) 25
   • C) 19
   • D) 23
5. 5.

   Triangle $ABC$ is similar to triangle $DEF$ such that the ratio of their corresponding sides is $\frac{AB}{DE} = \frac{3}{5}$. If the area of triangle $ABC$ is $54\text{ cm}^2$, what is the area of triangle $DEF$?

   • A) $90\text{ cm}^2$
   • B) $150\text{ cm}^2$
   • C) $250\text{ cm}^2$
   • D) $300\text{ cm}^2$

Answers and step-by-step solutions appear after you finish the test.