what additional information is needed to prove that the triangles are congruent using the asa congruence…

what additional information is needed to prove that the triangles are congruent using the asa congruence theorem?\n○ $overline{nl}congoverline{mp}$\n○ $overline{nk}congoverline{mq}$\n○ $angle ncongangle m$\n○ $angle lcongangle p$

what additional information is needed to prove that the triangles are congruent using the asa congruence theorem?\n○ $overline{nl}congoverline{mp}$\n○ $overline{nk}congoverline{mq}$\n○ $angle ncongangle m$\n○ $angle lcongangle p$

Answer

Explanation:

Step1: Recall ASA congruence theorem

ASA (Angle - Side - Angle) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

Step2: Analyze given information

We can assume some right - angled triangles with some equal sides shown by tick marks. We need an equal angle that is between the sides that are already potentially equal.

Step3: Check each option

  • $\overline{NL}\cong\overline{MP}$ is about sides, not angles for ASA.
  • $\overline{NK}\cong\overline{MQ}$ is about sides, not angles for ASA.
  • $\angle N\cong\angle M$ is the correct angle as it is the included angle between the sides that might be equal based on the tick - marks in the triangles, which satisfies ASA.
  • $\angle L\cong\angle P$ is not the included angle for the sides that are likely to be equal for ASA.

Answer:

C. $\angle N\cong\angle M$