Question

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

Explanation:

Step1: Identify right - angled triangles

The two triangles $\triangle ABC$ and $\triangle DEF$ are right - angled triangles as $\angle A=\angle D = 90^{\circ}$.

Step2: Analyze congruence postulates

• HL (Hypotenuse - Leg): We don't know the hypotenuse lengths, so we can't use HL.
• SAS (Side - Angle - Side): There is no information about the included side between the angles, so we can't use SAS.
• LA (Leg - Angle): We have a pair of right angles ($\angle A=\angle D$) and a pair of corresponding legs are equal (shown by the single tick marks on the legs), so LA can be used.
• AAS (Angle - Angle - Side): We have a right - angle, another pair of angles (the non - right angles shown equal) and a non - included side (the legs shown equal), so AAS can be used.
• HA (Hypotenuse - Angle): We don't know the hypotenuse lengths, so we can't use HA.
• LL (Leg - Leg): We have one pair of legs shown equal, but no information about the other pair of legs, so we can't use LL.

Answer:

C. LA
D. AAS