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?

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.

Answer 1

the actual answer is D

Explanation:

they are congruent lol, i also took the unit test and got 100 on edge

Answer 2

Yes, there is a series of rigid transformations that can map ΔQRS to ΔABC. ΔQRS can be translated so that R is mapped to B and then rotated to align S with C. This preserves side lengths, angles, and parallelism, making ΔQRS congruent to ΔABC.

Option C is correct.

To determine if there is a series of rigid transformations that could map ΔQRS to ΔABC, we need to examine the given information.

Sides and Angles: ΔQRS and ΔABC have corresponding sides with equal lengths (16 cm and 24 cm) and right angles at QRS and ABC.

Parallel Sides: QS and AC are parallel and identical.

Considering these properties, the triangles are not only congruent but also share a similar orientation. Therefore, there is a series of rigid transformations that could map ΔQRS to ΔABC.

The correct transformation sequence is as follows:

Translation: ΔQRS can be translated so that R is mapped to B. This accounts for the common side RS = BC.

Rotation: After translation, a rotation can be applied to align S with C. This rotation ensures that the corresponding sides and angles match.

Thus, the correct choice is:

Yes, ΔQRS can be translated so that R is mapped to B and then rotated so that S is mapped to C.

This sequence of transformations preserves the side lengths, angles, and parallelism, making ΔQRS congruent to ΔABC.