Complete a coordinate proof to show that the triangles created by the keyboard stand are congruent.
A figure shows a keyboard stand. Two line segments are drawn on the coordinate plane. The line segment P S and line segment Q T intersect at point R. The x-axis is extended from 0 to 24, in increments of 6. The y- axis is extended from 0 to 30, in increments of 6. Vertex P lies at the ordered pair 3 comma 30. Vertex Q lies at the ordered pair 21 comma 30. Vertex T lies at the ordered pair 3 comma 0. Vertex S lies at the ordered pair 21 comma 0. Vertex R lies at the ordered pair 12 comma 15.
Put responses in the correct response input area to answer the question. Select a response, navigate to the desired input area and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The horizontal segments $\overline{PQ}$ and $\overline{ST}$ each have a slope of Response input area, which implies that they are parallel. Also, because $PQ\ =$ Response input area $=\ \abs{21-3}=$ Response input area, $\overline{PQ}\cong$ Response input area.
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