Question

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

Answer 1

Yes, a translation mapping R to B followed by a rotation aligning S with C preserves the size and shape of ΔQRS, mapping it to ΔABC. Option (c) is correct.

Yes, there is a series of rigid transformations that could map ΔQRS to ΔABC. First, a translation can be applied to ΔQRS so that point R coincides with point B. After the translation, a rotation can be performed to align point S with point C. Since both triangles have a right angle at Q and B, this sequence of rigid transformations—translation followed by rotation—preserves the size and shape of the triangles.

The translation maintains the parallelism of sides QS and AC, and the rotation ensures that the angles and side lengths are preserved. Therefore, the correct option is (c): Yes, ΔQRS can be translated so that R is mapped to B and then rotated so that S is mapped to C.