Congruence and similarity Knowledge-Based Download PDF

Questions

1. 1.

   Which of the following conditions is sufficient to guarantee that two triangles are congruent?

   • A) Three pairs of congruent corresponding angles (AAA)
   • B) Two pairs of congruent corresponding sides and the included angle between them (SAS)
   • C) Two pairs of congruent corresponding sides and a non-included angle (SSA)
   • D) Equal areas and one pair of congruent corresponding angles
2. 2.

   Two similar polygons have perimeters of 32 cm and 48 cm. If the shortest side of the smaller polygon has a length of 6 cm, what is the length of the corresponding shortest side of the larger polygon?

   • A) 8 cm
   • B) 9 cm
   • C) 12 cm
   • D) 15 cm
3. 3.

   Given that $\triangle ABC \cong \triangle JKL$, with $AB = 3x - 4$, $JK = x + 8$, and $BC = 2x + 1$, what is the length of side $KL$?

   • A) 6
   • B) 11
   • C) 13
   • D) 14
4. 4.

   In triangles $\triangle PQR$ and $\triangle STU$, $\angle P = 55^\circ$, $\angle Q = 75^\circ$, $\angle S = 55^\circ$, and $\angle U = 50^\circ$. If $PQ = 8\text{ cm}$, $QR = 6\text{ cm}$, and $TU = 9\text{ cm}$, what is the length of side $ST$?

   • A) 10 cm
   • B) 12 cm
   • C) 14 cm
   • D) 16 cm
5. 5.

   Triangles $\triangle ABC$ and $\triangle DEF$ are similar such that the ratio of their corresponding side lengths is $3 : 5$. If the area of $\triangle ABC$ is $54\text{ cm}^2$, what is the area of $\triangle DEF$?

   • A) $90\text{ cm}^2$
   • B) $125\text{ cm}^2$
   • C) $150\text{ cm}^2$
   • D) $270\text{ cm}^2$