Question

triangles abc and def have the following characteristics:
∠b and ∠e are right angles
∠a ≅ ∠d
\overline{bc} ≅ \overline{ef}
which congruence theorem can be used to prove △abc ≅ △def?
○ aas
○ asa
○ hl
○ sas

Explanation:

• AAS (Angle - Angle - Side):
• In right - angled triangles \( \triangle ABC\) (\(\angle B = 90^{\circ}\)) and \( \triangle DEF\) (\(\angle E=90^{\circ}\)), we have two angles (\(\angle A\cong\angle D\) and \(\angle B\cong\angle E\)) and a non - included side (\(BC\cong EF\)).
• The AAS congruence theorem states that 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, then the two triangles are congruent.
• ASA (Angle - Side - Angle):
• For ASA, the side should be included between the two angles. Here, the side \(BC\) (or \(EF\)) is not included between \(\angle A\) and \(\angle B\) (or \(\angle D\) and \(\angle E\)).
• HL (Hypotenuse - Leg):
• HL requires information about the hypotenuse and a leg. We are not given any information about the hypotenuse of the right - angled triangles.
• SAS (Side - Angle - Side):
• For SAS, the angle should be included between the two sides. We are not given information about two sides with an included angle.

Answer:

AAS