Question

question 2 of 10
based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why △joy≅△lim?
check all that apply.
a. ha
b. aas
c. asa
d. ll
e. hl
f. la

Explanation:

• HA (Hypotenuse - Angle):
• In right - angled triangles, if the hypotenuse and an acute angle of one right - triangle are equal to the hypotenuse and an acute angle of another right - triangle, the triangles are congruent. Here, we have right - angled triangles \(\triangle JOY\) and \(\triangle LIM\) (\(\angle Y=\angle M = 90^{\circ}\)). If we assume the hypotenuse (the non - leg side) and an acute angle (say \(\angle J=\angle L\)) are equal (from the diagram's visual cues of equal markings for angles and sides in the right - triangle context), HA can be used.
• AAS (Angle - Angle - Side):
• We have two right angles (\(\angle Y=\angle M = 90^{\circ}\)), and if two other angles (one non - right angle in each triangle, say \(\angle J=\angle L\) and \(\angle O=\angle I\)) and a non - included side (the hypotenuse or a leg) are equal. In the right - triangle context, for two right - angled triangles, if two angles (one right angle and one acute angle) and a non - included side (can be a leg or hypotenuse) are equal, AAS can be applied.
• LL (Leg - Leg):
• For right - angled triangles, if the two legs of one right - triangle are equal to the two legs of another right - triangle, the triangles are congruent. If we assume from the diagram that the legs of \(\triangle JOY\) and \(\triangle LIM\) are equal (by visual side - marking cues in the right - triangle setup), LL can be used.
• LA (Leg - Angle):
• In right - angled triangles, if a leg and an acute angle of one right - triangle are equal to a leg and an acute angle of another right - triangle, the triangles are congruent. If we assume a leg (say \(JY = LM\)) and an acute angle (say \(\angle J=\angle L\)) are equal (from diagram markings), LA can be used.

Answer:

A. HA, B. AAS, D. LL, F. LA