Question

The triangles are congruent by the SSS congruence theorem. Which transformation(s) can map BCD onto WXY? rotation only reflection only translation, then rotation translation, then reflection

Answer 1

Answer: The correct transformations are translation, then rotation.

Step-by-step explanation: Given that the triangles BCD and WXY are congruent by SSS congruence theorem.

We are given to choose the correct transformations that can map ΔBCD onto ΔWXY.

According to the given information in the figure, the pairs of corresponding vertices of both the triangles are (B, W), (C,X) and (D, Y).

At first, we will translate ΔBCD vertically and horizontally by particular units, so that the vertex 'D' of ΔBCD coincides with the corresponding vertex 'Y' of ΔWXY.

After that, we will rotate ΔBCD anticlockwise about the common vertex 'D' or 'Y' through an angle of 90°, so that all the corresponding sides of ΔBCD and ΔWXY coincide with each other.

Therefore, the correct transformations are translation, then rotation.

Thus, (C) is the correct option.

Answer 2

Translation then rotation

Explanation:

When transforming the geometric shapes

rotation means turn,

reflection means flip,

translation means slide/move.

Here, we see that ΔBCD can be mapped on ΔWXY by rotating the former counterclockwise and sliding it. Or the same can be achieved by first sliding the triangle and then rotating it counterclockwise.

Hence the answer is translation then rotation.