Question

question 6 of 10
based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why △def≅△jkl?
check all that apply.
a. la
b. asa
c. hl
d. sas
e. ll
f. aas

Explanation:

Step1: Analyze LA (Leg - Angle)

In right - angled triangles, if a leg and an acute angle of one right - triangle are equal to the corresponding leg and acute angle of another right - triangle, the triangles are congruent. Here, we have right - angled triangles (\(\angle D=\angle J = 90^{\circ}\)), a leg (marked as equal) and an acute angle (marked as equal).

Step2: Analyze AAS (Angle - Angle - Side)

We have two angles (one right angle and one marked acute angle) and a non - included side (the marked leg). For AAS, if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, the triangles are congruent.

Step3: Analyze LL (Leg - Leg)

Since they are right - angled triangles, if two legs of one right - triangle are equal to two legs of another right - triangle, by LL (in right - angled triangle congruence, which is a special case of SAS for right - angled triangles), the triangles are congruent. The marked leg is one pair of equal legs, and the other pair of legs (the sides adjacent to the right angle which are also equal as per the congruence conditions from angles and side relationships in right - angled triangles)

Answer:

A. LA, E. LL, F. AAS