Question

Two streets intersect at a 30- degree angle. At the intersection, the are four crosswalks formed that are the same length. what type of quadrilateral is formed by the crosswalks?

Answer 1

The quadrilateral thus formed is a rhombus also known as equilateral quadrilateral.

Explanation:

For better understanding of the explanation see the attached figure :

In the given figure : When the two streets intersect, the quadrilateral thus formed is PQRS which is marked with blue color.

Now, the four crosswalks thus formed are parallel in pairs, because they are both normal to the same two parallel lines.

⇒ PQ is parallel to RS and PS is parallel to QR (Because in Euclidean Geometry, two lines normal to the same line are parallel).

Thus, PQRS is a parallelogram with equal sides.

Now it can be either rhombus or a square.

But one angle of PQRS is given to be 30° and since each angle of square is 90°. So, PQRS cannot be a square.

Hence, the quadrilateral thus formed is a rhombus also known as equilateral quadrilateral.