1. Parallel Lines

I got the following problem as homework in my class:

In the figure given below, l is parallel to m, p is parallel to q, p is perpendicular to l & q is perpendicular to m. What can you say about the quadrilateral ABCD in the figure? Is it a rectangle? Justify your answer.

Thanks,

Ron

2. Hello Ron
Originally Posted by rn5a
I got the following problem as homework in my class:

In the figure given below, l is parallel to m, p is parallel to q, p is perpendicular to l & q is perpendicular to m. What can you say about the quadrilateral ABCD in the figure? Is it a rectangle? Justify your answer.

Thanks,

Ron
Yes, it is a rectangle.

A quadrilateral is a rectangle if all its angles are right-angles. Using the fact that p is perpendicular to l and l is parallel to m is sufficient to prove that p is perpendicular to m (corresponding angles equal). Three of the angles of ABCD are now known to be right-angles. Therefore the fourth is also a right-angle (angle sum of quadrilateral). Therefore ABCD is a rectangle.

3. Thanks mate for your response but in a rectangle, the 2 lengths are equal & the 2 breadths are equal whereas in a square, all the 4 sides are equal. So why is the quadrilateral ABCD a rectangle, why not a square? Moreover can't a quadrilateral be a square if all the angles are right-angled?

Thanks,

Ron

4. Hello Ron
Originally Posted by rn5a
Thanks mate for your response but in a rectangle, the 2 lengths are equal & the 2 breadths are equal whereas in a square, all the 4 sides are equal. So why is the quadrilateral ABCD a rectangle, why not a square? Moreover can't a quadrilateral be a square if all the angles are right-angled?

Thanks,

Ron
Yes, it can be a square. A square is just a special sort of rectangle, that's all.

When you say someone is a European, that doesn't mean that they can't be British. Similarly, if you say a shape is a rectangle, it doesn't mean it can't be a square. The set of squares is a subset of the set of rectangles.