Question

In the figure, the horizontal lines parallel and PQ=RS. Find XU

Answer 1

The value of XU is 3.

First, we can see that triangles TPQ, QRU, and RSV are all congruent right triangles, since they each have a 90-degree angle and a 45-degree angle.

Next, we can see that triangles TXU, UYV, and VZS are also all congruent right triangles, since they each have a 90-degree angle and a 45-degree angle.

Now, we can see that triangle TPR is made up of triangles TPQ and QRU, and triangle USV is made up of triangles UYV and VZS. Therefore, triangle TPR is congruent to triangle USV.

Finally, we can see that XU is the hypotenuse of triangle TXU, and PR is the hypotenuse of triangle TPR. Since triangle TXU is congruent to triangle TPR, we know that XU=PR.

Therefore, the value of XU is 3.

Answer 2

Given that:

PQ = QR = RS, YW = 2.25,

Since the horizontal lines are parallel,

`TX=XZ=ZU`