Question

name two triangles that are congruent by asa

choose the correct answer below

△mnp≅△qrs
△qrs≅△tuv
△mnp≅△tuv

Explanation:

Step1: Recall ASA congruence criterion

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

• For \(\triangle MNP\) and \(\triangle TUV\):
• In \(\triangle MNP\), we have a right - angle (\(\angle P = 90^{\circ}\)), and two sides (the legs of the right - triangle which are equal as per the markings).
• In \(\triangle TUV\), we have a right - angle (\(\angle V=90^{\circ}\)), and the two sides (the legs of the right - triangle which are equal as per the markings).
• The right - angle is the included angle between the two equal sides in both right - triangles.

Step2: Check other options

• For \(\triangle MNP\) and \(\triangle QRS\): \(\triangle MNP\) is a right - triangle (\(\angle P = 90^{\circ}\)) and \(\triangle QRS\) is not a right - triangle. So, they cannot be congruent by ASA.
• For \(\triangle QRS\) and \(\triangle TUV\): \(\triangle QRS\) is not a right - triangle and \(\triangle TUV\) is a right - triangle. So, they cannot be congruent by ASA.

Answer:

\(\triangle MNP\cong\triangle TUV\)