Question

State whether the following statements are true or false, and explain your reasoning.

a) A square is a rectangle.
b) A polygon with 21 sides has 432 possible diagonals.
c) All three angles in an Isosceles triangle are equal.
d) The measures of the exterior angles of a nonagon, a nine-sided figure, have a sum of 360°.

Answer 1

Explanation:

a) A square is a rectangle. True

Reason: Property of Rectangle: (i) Opposite sides are equal and parallel. (ii) Each angle is 90 (iii) Diagonals are equal and bisect each other.

A square hold all these properties. A square is a rectangle.

b) A polygon with 21 sides has 432 possible diagonals. False

Reason: Number of diagonals of a polygon =
`(n(n-3))/(2)`

n --> number of sides of a polygon.

=
`(21*18)/(2)` = 189 diagonals

c) All three angles in an Isosceles triangle are equal. False

Reason: In an isosceles triangle, two angles are equal.

If three angles are equal, then that is an equilateral triangle.

d) The measures of the exterior angles of a nonagon, a nine-sided figure, have a sum of 360°. True.

Reason: The sum of measures of the exterior angles of any polygon is 360