Mathematics : Understanding Quadrilaterals

The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm.)

In the following figure, both RISK and CLUE are parallelogram. Find the value of x.

State whether True or False.

A.

All rectangles are squares.

B.

All rectangles are squares.

C.

All square are rhombuses and also rectangles.

D.

All square are rhombuses and also rectangles.

E.

All kites are rhombuses.

F.

All rhombuses are kites.

G.

All parallelograms are trapeziums.

H.

 All squares are trapeziums.

Identify all the quadrilaterals that have:

(a) Four sides of equal length. (b) Four right angles.

Explain how a square is:

(i) a quadrilateral (ii) a parallelogram

(iii) a rhombus (iv) a rectangle

Name the quadrilaterals whose diagonal:

(i) bisect each other (ii) are perpendicular bisectors of each other

(iii) are equal

Explain why a rectangle is a convex quadrilateral.

ABC is a right-angled triangle and O is the mid-point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally by to help you.)

A mason has made a concrete slab. He needs it to be rectangular. In what different ways can he make sure that it is rectangular?

A square was defined as a rectangle with all sides equal. Can we define it as rhombus with equal angles? Explore this idea.