Answer:
- PS = 3
- SR = 3
- PQ = √29
- QR = √29
- 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
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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
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5)
The figure has two pairs of congruent adjacent sides, so is a kite.
