Triangle congruence (SSS, SAS, ASA, AAS, HL) and proofs Knowledge-Based Download PDF

Questions

1. 1.

   In quadrilateral ABCD, it is given that $\overline{AB} \cong \overline{CD}$ and $\overline{BC} \cong \overline{DA}$. Which congruence criterion directly proves that $\triangle ABC \cong \triangle CDA$?

   • A) Angle-Side-Angle (ASA)
   • B) Side-Angle-Side (SAS)
   • C) Hypotenuse-Leg (HL)
   • D) Side-Side-Side (SSS)
2. 2.

   In quadrilateral $ABCD$, diagonal $\overline{AC}$ bisects both $\angle BAD$ and $\angle BCD$. Which congruence criterion directly proves that $\triangle ABC \cong \triangle ADC$?

   • A) ASA (Angle-Side-Angle)
   • B) SAS (Side-Angle-Side)
   • C) SSS (Side-Side-Side)
   • D) AAS (Angle-Angle-Side)
3. 3.

   In $\triangle ABC$ and $\triangle DEF$, $\angle B$ and $\angle E$ are right angles. Which of the following conditions is sufficient to prove that $\triangle ABC \cong \triangle DEF$ using the Hypotenuse-Leg (HL) congruence theorem?

   • A) $\overline{AB} \cong \overline{DE}$ and $\angle A \cong \angle D$
   • B) $\overline{AC} \cong \overline{DF}$ and $\overline{BC} \cong \overline{EF}$
   • C) $\overline{AB} \cong \overline{DE}$ and $\overline{BC} \cong \overline{EF}$
   • D) $\angle A \cong \angle D$ and $\angle C \cong \angle F$
4. 4.

   In $\triangle JKL$ and $\triangle XYZ$, it is given that $\angle J \cong \angle X$, $\angle K \cong \angle Y$, and $\overline{JL} \cong \overline{XZ}$. Which congruence criterion directly proves that $\triangle JKL \cong \triangle XYZ$?

   • A) AAS (Angle-Angle-Side)
   • B) ASA (Angle-Side-Angle)
   • C) SAS (Side-Angle-Side)
   • D) SSS (Side-Side-Side)
5. 5.

   In $\triangle PQR$ and $\triangle STU$, it is given that $\overline{PQ} \cong \overline{ST}$ and $\angle P \cong \angle S$. Which additional condition is sufficient to prove that $\triangle PQR \cong \triangle STU$ by the SAS (Side-Angle-Side) congruence criterion?

   • A) $\angle Q \cong \angle T$
   • B) $\overline{QR} \cong \overline{TU}$
   • C) $\overline{PR} \cong \overline{SU}$
   • D) $\angle R \cong \angle U$