Question

question 7 of 10
based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why ( \triangle joycong\triangle lim )?
check all that apply.

a. la
b. ha
c. hl
d. aas
e. asa
f. ll

Explanation:

• LA (Leg - Angle): For right - angled triangles, if a leg and an acute angle of one right - triangle are congruent to the corresponding leg and acute angle of another right - triangle, the triangles are congruent. In \(\triangle JOY\) and \(\triangle LIM\), we can assume the right angles (\(\angle Y\) and \(\angle M\)) and a pair of legs (the marked equal sides) along with a pair of acute angles (the non - right angles) satisfy this condition.
• AAS (Angle - Angle - Side): If two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, the triangles are congruent. Here, the two right angles (\(\angle Y\cong\angle M\)), a pair of non - right angles (the non - right angles of the triangles) and a pair of sides (the marked equal sides) satisfy this.
• ASA (Angle - Side - Angle): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. We can consider the two non - right angles (as angles) and the marked equal side (as the included side) between them for the two right - angled triangles.
• LL (Leg - Leg): For right - angled triangles, if the two legs of one right - triangle are congruent to the two legs of another right - triangle, the triangles are congruent. The marked equal sides (which are legs) and the right angles (implied for the right - angled triangles) make this applicable.

The HA (Hypotenuse - Angle) and HL (Hypotenuse - Leg) theorems require information about the hypotenuse (which is not given in the basic problem description as we only know about legs and non - hypotenuse sides from the marking).

Answer:

A. LA, D. AAS, E. ASA, F. LL