Question

1. determine whether each statement is true or false. if it is false,

explain why.
a. a square is also a rectangle.
b. a rectangle is also a square.
c. a parallelogram is also a trapezoid.
d. the diagonals of a trapezoid are congruent.
e. a kite is also a parallelogram.
f. the diagonals of a rhombus bisect each other.

Explanation:

• a. A square is also a rectangle: A square has all the properties of a rectangle (four right - angles and opposite sides equal and parallel). So, this statement is true.
• b. A rectangle is also a square: A rectangle does not necessarily have all sides equal (a requirement for a square). So, this statement is false.
• c. A parallelogram is also a trapezoid: A parallelogram has two pairs of parallel sides, while a trapezoid has only one pair of parallel sides. So, this statement is false.
• d. The diagonals of a trapezoid are congruent: Only in an isosceles trapezoid the diagonals are congruent. For a general trapezoid, this is not true. So, this statement is false.
• e. A kite is also a parallelogram: A kite has two pairs of adjacent sides equal, but in a parallelogram, opposite sides are equal. So, this statement is false.
• f. The diagonals of a rhombus bisect each other: One of the properties of a rhombus is that its diagonals bisect each other at right angles. So, this statement is true.

Answer:

a. True; b. False; c. False; d. False; e. False; f. True