Question

is △abc ≅ △def? explain.
4 - 5: lesson quiz

Explanation:

Step1: Identify the right - angled triangles

Both \(\triangle ABC\) and \(\triangle DEF\) are right - angled triangles (\(\angle C=\angle F = 90^{\circ}\)).

Step2: Check the side - side - side (SAS) congruence condition

In \(\triangle ABC\) and \(\triangle DEF\), we have two pairs of corresponding sides equal. Let's assume \(AB = DE\) (hypotenuse) and \(AC=DF\) (one of the legs).
By the SAS (Side - Angle - Side) congruence criterion for right - angled triangles (the right angle is the included angle between the leg and the hypotenuse in a right - angled triangle context for SAS in the case of right - angled triangles, we can also think of it as a special case of SAS where the angle is \(90^{\circ}\)).

Answer:

Yes, the triangles are congruent by SAS.