Chapter Test
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If the polygons are similar, you should be able to map one polygon on top of the other by using similarity transformations.
Similar
Explanation: See solution.
Let's start by graphing QRST and WXYZ.
From the diagram we see that the orientation of WXYZ is upside down compared to QRST. To make sure the two trapezoids have the same orientation, we can reflect QRST in the x-axis which turns the trapezoid upside down.
Next, we will have to translate Q'R'S'T' so that two corresponding vertices map onto each other. If we translate it 2 units to the right and 4 units down, we can map T' onto Z. Notice that a translation is a rigid motion which means that angle and side measures are preserved.
Finally, by dilating Q''R''S''T'' with some scale factor we can make it the same size as WXYZ. To find this scale factor, we have to measure the length of two corresponding sides.
As we can see ZY is 155=3 times longer than T''S''. Therefore, we have to dilate Q''R''S''T'' with a scale factor of 3 to make it the same size as WXYZ. Note that to map it to WXYZ we should use T'' as the center of dilation.
Since we were able to map one image onto the other, the shapes are similar.