Question

Identify the true statements:
A. A rectangle is a parallelogram.
B. A square is a radius.
C. A parallelogram is a rhombus.
D. A kite is a parallelogram.

Answer 1

Hint:
In this question, we have to identify the true statement given for quadrilateral. For this, we will understand the properties of the quadrilateral and then compare every statement to check if it is true or not. We will also try to draw figures for each quadrilateral.

Complete step by step answer:
Here we are given the four statements, let us analyze them one by one.
A. A rectangle is a parallelogram.
We know that a parallelogram is a four sided figure (quadrilateral) whose opposite sides are parallel and equal. A parallelogram looks like below and also let us draw a diagram for the rectangle.

As we can see, a rectangle has also opposite sides as parallel and equal. Therefore, we can say that a rectangle is a parallelogram.
B. A square is a rhombus.
We know that a rhombus is a four-sided figure (quadrilateral) whose all four sides are equal i.e. opposite sides, as well as adjacent sides, are equal.
A rhombus looks like the below figure and lets us draw a diagram for a square.

As we can see, a square also has all four sides equal. Therefore, we can say that a square is a rhombus.
C. A parallelogram is a rhombus.
From the previously stated definition, we see that a rhombus has all four sides equal whereas a parallelogram has only opposite sides equal. Parallelogram does not have adjacent sides equal. Therefore, a parallelogram is not a rhombus.
D. A kite is a parallelogram.
A kite is a quadrilateral whose one pair of adjacent sides is equal to each other and the other pair of adjacent sides is equal to each other.
A parallelogram has opposite sides equal.
Therefore, a kite is not a parallelogram. A kite looks like this,

Hence option A and option B are the correct answers.

Note:
Students should keep in mind the major properties of all quadrilateral. They should note that a parallelogram has opposite sides equal, a rhombus has all four sides equal, whereas a kite has adjacent pairs equal. Square is a rhombus with each angle to ${{90}^{\circ }}$. The rectangle is a parallelogram with each angle equal to ${{90}^{\circ }}$.