Question

7 multiple choice 1 point state what additional information is needed to prove the triangles are congruent using asa:

mk ≅ su
lk ≅ tu
∠k ≅ ∠u
∠l ≅ ∠t

Explanation:

Step1: Recall ASA (Angle - Side - Angle) Congruence Criterion

ASA states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Step2: Analyze the Given Information

We already have one pair of congruent angles (\(\angle M\cong\angle S\)) and one pair of congruent sides (the marked sides). For ASA, we need another pair of congruent angles.

Step3: Check Each Option

• \(MK\cong SU\): This is a side, but we need an angle for ASA.
• \(LK\cong TU\): This is a side, not an angle for ASA.
• \(\angle K\cong\angle U\): If \(\angle K\cong\angle U\), along with the already - known \(\angle M\cong\angle S\) and the marked congruent sides (included side between the angles), we can apply ASA.
• \(\angle L\cong\angle T\): This is not the included angle for the marked side.

Answer:

\(\angle K\cong\angle U\) (the third option)