Question

triangles mtk and fsn are shown, where mt ⊥ km, fs ⊥ nf, mk ≅ fn, and mt ≅ fs. what congruence postulate or theorem can be used to prove △mtk ≅ △fsn?
○ sas congruence
○ aas congruence
○ asa congruence
○ hl congruence

Explanation:

Step1: Recall triangle congruence criteria

There are several triangle congruence criteria: SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), SSS (Side - Side - Side), and HL (Hypotenuse - Leg) for right - angled triangles.

Step2: Identify the type of triangles

Since \(MT\perp KM\) and \(FS\perp NF\), \(\triangle MTK\) and \(\triangle FSN\) are right - angled triangles.

Step3: Apply the HL criterion

The HL (Hypotenuse - Leg) criterion states that if the hypotenuse and a leg of one right - angled triangle are congruent to the hypotenuse and a leg of another right - angled triangle, then the two triangles are congruent. Here, \(MK\cong FN\) (leg) and \(MT\cong FS\) (leg). So, the HL congruence postulate can be used to prove \(\triangle MTK\cong\triangle FSN\).

Answer:

A. HL Congruence