Question

State whether true or false.
a]All rectangles are squares.
b]All rhombuses are parallelograms.
c]All squares are rhombuses and also rectangles.
d]All squares are not parallelograms.
e]All kites are rhombuses.
f]All rhombuses are kites.
g]All parallelograms are trapeziums.
h]All squares are trapeziums.

Answer 1

Hint: Mathematics includes the study of topics which are related to quantity structure , space and change. One of the most important branches of mathematics is geometry. It includes the analysis of figures using simple theorems and results. In this problem we have to critically analyse the statement and determine its truth value.

Complete step-by-step answer:
a] It yields a false result as all squares are rectangles. A rectangle can have two values of dimensions, while a square has only one value.
b] It yields a true result as both rhombuses and parallelograms have two opposite sides which are also parallel.
c] It yields a true result as all the properties of rhombuses and rectangles are satisfied by square.
d] It yields a false result as a parallelogram has opposite sides equal and parallel which is true for square also.
e] It yields a false result. Kites seem to be rhombus but their actual dimensions of each pair of sides are different.
f] It yields a true result. Rhombus can somehow satisfy the criteria of being kite because it has two consecutive pairs of equal length.
g] It yields a true result because both the figures have one pair of parallel sides.
h] It yields a true result because both the figures have one pair of parallel sides.
Note: The key step for solving this problem is the knowledge of various geometrical figures and properties associated with them. By using this knowledge, we can easily classify and relate the pair of figures given in the question.