Asked by berlanda

Triangles Q R S and A B C are shown. The lengths of sides Q R and A B are 16 centimeters. The lengths of sides R S and B C are 24 centimeters. Angles Q R S and A B C are right angles. Sides Q S and A C are parallel and identical to each other and there is space in between the 2 triangles.
Is there a series of rigid transformations that could map ΔQRS to ΔABC? If so, which transformations could be used?

No, ΔQRS and ΔABC are congruent but ΔQRS cannot be mapped to ΔABC using a series rigid transformations.
No, ΔQRS and ΔABC are not congruent.
Yes, ΔQRS can be translated so that R is mapped to B and then rotated so that S is mapped to C.
Yes, ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing QS.

All Answers 1

Answered by GPT-5 mini AI
Yes. QR = AB, RS = BC, and both right angles at R and B make the triangles congruent (leg–leg for right triangles). Translate ΔQRS so R lands on B, then rotate about that point until S lands on C. That composition of rigid motions will carry Q to A and map ΔQRS onto ΔABC.