Q.7 - EXERCISE 3.3 - Chapter 3 Understanding Quadrilaterals - NCERT CLASS 8 Math Solutions Full

7. The adjacent figure HOPE is a parallelogram. Find the angle measures
x, y and z. State the properties you use to find them.
1. Given a parallelogram ABCD. Complete each
statement along with the definition or property used.
2. Consider the following parallelograms. Find the values of the unknowns x, y, z.
3. Can a quadrilateral ABCD be a parallelogram if
(i) ∠D + ∠B = 180°? (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?
(iii) ∠A = 70° and ∠C = 65°?
4. Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles
of equal measure.
5. The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each
of the angles of the parallelogram.
6. Two adjacent angles of a parallelogram have equal measure. Find the
measure of each of the angles of the parallelogram.
8. The following figures GUNS and RUNS are parallelograms.
Find x and y. (Lengths are in cm)
9. In the above figure both RISK and CLUE are parallelograms. Find the value of x.
10. Explain how this figure is a trapezium. Which of its two sides are parallel? (Fig 3.32)
11. Find m∠C in Fig 3.33 if AB DC .
12. Find the measure of ∠P and ∠S if SP RQ in Fig 3.34.
(If you find m∠R, is there more than one method to find m∠P?)
These questions have been fully solved in this video .
Here are the basic concepts which are required to solve all these questions.
Kinds of Quadrilaterals
Based on the nature of the sides or angles of a quadrilateral, it gets special names.
Trapezium
Trapezium is a quadrilateral with a pair of parallel sides.
Study the above figures and discuss with your friends why some of them are trapeziums
while some are not. (Note: The arrow marks indicate parallel lines).
Kite
Kite is a special type of a quadrilateral. The sides with the same markings in each figure
are equal. For example AB = AD and BC = CD.
Study these figures and try to describe what a kite is. Observe that
(i) A kite has 4 sides (It is a quadrilateral).
(ii) There are exactly two distinct consecutive pairs of sides of equal length.
Parallelogram
A parallelogram is a quadrilateral. As the name suggests, it has something to do with
parallel lines.
Study these figures and try to describe in your own words what we mean by a
parallelogram. Share your observations with your friends.
Check whether a rectangle is also a parallelogram.
Elements of a parallelogram
There are four sides and four angles in a parallelogram. Some of these are
equal. There are some terms associated with these elements that you need
to remember.
Given a parallelogram ABCD (Fig 3.18).
AB and DC, are opposite sides. AD and BC form another pair of opposite sides.
∠A and ∠C are a pair of opposite angles; another pair of opposite angles would be
∠B and ∠D.
AB and BC are adjacent sides. This means, one of the sides starts where the other
ends. Are BC and CD adjacent sides too? Try to find two more pairs of adjacent sides.
∠A and ∠B are adjacent angles. They are at the ends of the same side. ∠B and ∠C
are also adjacent. Identify other pairs of adjacent angles of the parallelogram.
Property: The opposite sides of a parallelogram are of equal length.
Property: The opposite angles of a parallelogram are of equal measure.
Property: The adjacent angles in a parallelogram are supplementary.
Diagonals of a parallelogram
The diagonals of a parallelogram, in general, are not of equal length.
(Did you check this in your earlier activity?) However, the diagonals
of a parallelogram have an interesting property.
Property: The diagonals of a parallelogram bisect each other (at the point of their
intersection, of course!)