What is the ratio of lengths of pr and qs is _: _

1:1

Your best option to solving these types of problems is to visualize aka sketch it out. So you draw two parallel lines, line PQ and line RS. It is also given that PR and QS are perpendicular to PQ and RS. By now you, you have a rectangle. Why is it a rectangle? A rectangle is a quadrilateral that has four right angles. The four sides are PQ, QS, SR, and PR and the four right angles are formed from the fact that the lines are perpendicular. Knowing that the figure described is a rectangle, we can also deduce that it is a parallelogram. A parallelogram, by definition, has equal opposite sides. That means that PQ has to equal RS in length, and PR has to equal QS in length. This means that the ratio is 1:1.

Hope this helps!

(Note, this does not actually mean each side is 1 in. or 1 cm. Since the sides are equal the ratio will always be simplified down to 1:1. For instance, x:x always simplifies to 1:1 because we divide x from both sides.)

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