Question

question 8 of 10
based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why △abc≅△xyz?
check all that apply.
a. sss
b. hl
c. la
d. ll
e. sas
f. asa

Explanation:

• LL (Leg - Leg): In right - angled triangles \(\triangle ABC\) and \(\triangle XYZ\) (since \(\angle C=\angle Z = 90^{\circ}\)), if the two legs are equal. From the diagram, we can assume the legs (the non - hypotenuse sides) are equal.
• LA (Leg - Angle): In right - angled triangles, if a leg and an acute angle are equal. Here, we have a right angle (\(\angle C=\angle Z = 90^{\circ}\)), and if we consider the given equal sides (legs) and the equal acute angles (the non - right angles, since the triangles have a pair of equal sides and right angles, we can use the fact that in right - angled triangles, if a leg and an acute angle are congruent).
• SAS (Side - Angle - Side): In right - angled triangles \(\triangle ABC\) and \(\triangle XYZ\), if two sides and the included angle are equal. The right angle is the included angle between the two legs. If the legs are equal, then by SAS (since the right angle is \(90^{\circ}\) for both triangles and the legs are the sides adjacent to the right angle).

SSS (Side - Side - Side) is not applicable as we are not given information about the hypotenuse. HL (Hypotenuse - Leg) is not applicable as we are not given information about the hypotenuse. ASA (Angle - Side - Angle) is not the most straightforward here as we are mainly dealing with right - angled triangle congruence based on legs and angles related to right - angled triangles in the given diagram (the primary congruence postulates for right - angled triangles in this context are LL, LA, and SAS).

Answer:

C. LA, D. LL, E. SAS