Question

question 3 of 10
based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why \\( \triangle j o y \cong \triangle l i m \\)?
check all that apply.
a. ha
b. la
c. asa
d. aas
e. hl
f. ll

Explanation:

• HA (Hypotenuse - Angle):
• For right - angled triangles, if the hypotenuse and an acute angle of one right - triangle are congruent to the hypotenuse and an acute angle of another right - triangle, the triangles are congruent. In \(\triangle JOY\) and \(\triangle LIM\), we can assume the non - marked sides (hypotenuses) are congruent (as per the congruence of other parts) and the acute angles are congruent.
• AAS (Angle - Angle - Side):
• We have two pairs of congruent angles (\(\angle J\cong\angle L\), \(\angle O\cong\angle I\)) and a pair of non - included congruent sides (the sides that are marked as congruent).
• ASA (Angle - Side - Angle):
• We can also consider the right angles (\(\angle Y\cong\angle M = 90^{\circ}\)), a pair of congruent acute angles (\(\angle J\cong\angle L\)) and the pair of congruent sides (the marked sides).

Answer:

A. HA, C. ASA, D. AAS