How can ΔWXY be mapped to ΔMNQ?

Question

Triangles W X Y and M N Q are shown. The lengths of sides M N and W X are 18 centimeters. The lengths of sides Y W and M Q are 30 centimeters. Angles Y W X and N M Q are congruent. Triangle W X Y is slightly up and to the right of triangle M N Q. Angle Y W X is the bottom angle and angle N M Q is the left angle.

Translate vertex W to vertex M, then reflect across the line containing _______________.

Answer 1

To map triangle ΔWXY to triangle ΔMNQ, you can first translate vertex W to vertex M, which means moving W directly over to M without rotating it.

Next, after the translation, you need to reflect the triangle across a specific line to align the other vertices correctly. Given that angle YWX is congruent to angle NMQ, and considering their positions:

1. After translating W to M, vertex Y will need to be positioned correctly to correspond to vertex N.
2. To accomplish this, you would reflect the triangle across the line that passes through points M and Y, effectively aligning its other side with the corresponding side of triangle ΔMNQ.

So the complete statement would be:

Translate vertex W to vertex M, then reflect across the line containing segment MY.

This will correctly map triangle ΔWXY onto triangle ΔMNQ.