Question

is △mnl≅△qnl? why or why not? yes, they are congruent by either asa or aas. yes, they are both right triangles. no, ∠m is not congruent to ∠nlq. no, there are no congruent sides.

Explanation:

Step1: Find angle - MLN

In right - triangle MNL, one angle is 90° and ∠M = 58°. Using the angle - sum property of a triangle (the sum of interior angles of a triangle is 180°), we have ∠MLN=180°−90° - 58° = 32°.

Step2: Identify congruent elements

In \(\triangle MNL\) and \(\triangle QNL\), we have:

• \(\angle MNL=\angle QNL = 90^{\circ}\) (given by the right - angle symbol).
• \(LN\) is a common side (reflexive property).
• \(\angle MLN=\angle QLN = 32^{\circ}\) (from Step 1).

By the Angle - Side - Angle (ASA) congruence criterion (two angles and the included side of one triangle are congruent to two angles and the included side of another triangle), \(\triangle MNL\cong\triangle QNL\). Also, we could consider it as AAS (Angle - Angle - Side) since we have two pairs of angles and a non - included side (the common side \(LN\)).

Answer:

Yes, they are congruent by either ASA or AAS.