NCERT Solutions for Class 5th Maths Chapter 7 The kite, the parallelogram and the rectangle — Shapes from the Rhombus
Book page 98 Updated on2026-09-19
Q1.
How many different 4-sided shapes (quadrilaterals) can you make? Here are three possible shapes.
Answer
You can make 4 different four-sided shapes: a kite, a rectangle, and two different parallelograms. The book shows three of them.
Remember, each piece is the same right-angled triangle. Call its sides the short side, the long side and the slanting side. Two pieces can be joined along any pair of matching sides, and the second piece can be placed either as a mirror or turned half a turn.
Join along
Second piece placed as
Shape you get
slanting side
a mirror
Kite
slanting side
turned half a turn
Rectangle
short side
turned half a turn
Parallelogram (long one)
long side
turned half a turn
Parallelogram (flatter one)
Four quadrilaterals from the same two pieces. The dotted line is the join.
Why the shape changes: Only two things can change — which side you glue, and whether you flip the piece or turn it. A flip makes matching pairs next to each other, and that gives a kite. A half turn sends each side to the opposite side, and that gives a parallelogram or a rectangle.
Check it yourself: Whatever you make, its area is the same — two pieces are two pieces. Only the outline changes.
Q2.
Have you made a shape like the one shown on the right? This shape is called a kite. What do you notice about the sides of a kite? Side 1 = Side 2. Similarly, Side 3 = Side 4. These sides are called adjacent sides.The shape shown on the right on page 98, with its four sides numbered.
Answer
A kite has two pairs of equal sides, and the equal sides are next to each other. Sides that are next to each other are called adjacent sides.
In a kite the equal sides touch each other. In a parallelogram the equal sides are opposite each other.
Side 1 = Side 2 (a pair of adjacent sides) Side 3 = Side 4 (another pair of adjacent sides) But Side 1 is not equal to Side 3.
Why the kite comes out this way: You made it by folding one piece over onto the other like a mirror. The mirror line is the dotted line down the middle. Whatever is on the left is copied on the right — so the two short sides match and the two long sides match.
Where you have seen it: A real paper kite you fly at Makar Sankranti is exactly this shape. Two short sides at the top, two long sides at the bottom, and the stick runs down the mirror line.
Q3.
Measure the sides of each of these two quadrilaterals A and B. What do you notice? Are there any pairs of sides that are equal? Which pairs are equal — adjacent or opposite?
Answer
In both A and B, the sides that are equal are the opposite ones, not the adjacent ones.
What your ruler will show
Measure the four sides of A. The top and the bottom come out the same. The left and the right come out the same.
Measure the four sides of B. Same story — top matches bottom, left matches right.
Compare a side with the one next to it. They are not equal.
So the equal pairs are the opposite pairs.
Both shapes have their opposite sides equal. B has square corners as well.
In A: top = bottom, left = right → opposite sides equal In B: top = bottom, left = right → opposite sides equal A quadrilateral whose opposite sides are equal is called a parallelogram.
Why they are not kites: You built A and B by turning the second piece half a turn instead of flipping it. A half turn sends each side across to the far side, so the matching sides end up opposite each other, not next to each other.
Kite or parallelogram? Ask one question: Are the equal sides touching (adjacent) or facing (opposite)? Touching → kite. Facing → parallelogram.
Q4.
What types of angles do quadrilaterals A and B have? Which angles are equal in each of the above parallelograms?
Answer
In A the opposite angles are equal. In B all four angles are equal, and each one is a right angle — so B is a rectangle.
Shape
Types of angles
Which angles are equal
Name
A
Two sharp (acute) angles and two blunt (obtuse) angles
The two sharp ones are equal; the two blunt ones are equal — and each pair is opposite
Parallelogram
B
Four right angles
All four are equal
Rectangle
How to check without a protractor
Take the corner of a fresh sheet of paper. That corner is a right angle.
Hold it into each corner of B. It fits exactly every time — so all four angles of B are right angles.
Hold it into the corners of A. Two corners are smaller than the paper corner and two are larger. So A has no right angle.
Trace one sharp corner of A on tracing paper and slide it across to the opposite corner. It fits — those two angles are equal.
Why a rectangle is a special parallelogram: A rectangle already has opposite sides equal, which is what makes something a parallelogram. It has one extra gift on top — all its angles are right angles. So every rectangle is a parallelogram, but not every parallelogram is a rectangle.
The family tree so far: quadrilateral → parallelogram (opposite sides equal) → rectangle (and all angles right angles) → square (and all sides equal too).