Question

What kind of quadrilateral is PQRS? EXPLAIN YOUR REASONING.

Answer 1

Answer:

1. PS = 3
2. SR = 3
3. PQ = √29
4. QR = √29
5. kite

Step-by-step explanation:

A quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a kite.

Perhaps a more conventional definition of a kite is that it is a quadrilateral with two pairs of congruent adjacent sides.

1, 2)

The lengths PS and SR can be found by counting grid squares along the line segments. Each has a length of 3. They constitute one pair of congruent adjacent sides.

  PS = SR = 3

__

3, 4)

The lengths of PQ an QR can be found using the distance formula. Essentially, it uses the Pythagorean theorem to compute the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates. For PQ and QR, those differences are 2 and 5, so the lengths of those segments are √(2² +5²) = √29.

  PQ = QR = √29

__

5)

The figure has two pairs of congruent adjacent sides, so is a kite.