Question

Why is it that the statement "all rhombuses are squares" is false, but the statement "all squares are rhombuses" is true? Use an example to help with your explanation.

Answer 1

Explanation:

The following are properties of a rhombus:

i) All sides are equal

ii) The diagonals bisect each other at right angle.

iii) Diagonals bisect the angles

iv) Sum of consecutive angles is 180°

The following are properties of a square:

i) All sides are equal

ii) The diagonals bisect each other at right angle.

iii) Diagonals bisect the angles

iv) All angles are right angle

A rhombus is a square only when all its angles are right angles (90°) but all squares are rhombuses because squares have the same property as rhombuses(since All angles are right angles, consecutive angles would add up to 180°). Therefore all rhombuses are not squares but all squares are rhombuses