Understanding Quadrilaterals - Maths Class 8th - Ex 3.3 - Q5 & Q6 - Chapter 3 - NCERT - CBSE
Understanding Quadrilaterals - Maths Class 8th - Ex 3.3 - Question 5 - Question 6 - Chapter 3 - NCERT - CBSE
Full exercise on Understanding Quadrilaterals, fully solved. This is a video tutorial for 8th class NCERT CBSE students. For other educational stuff, subscribe and press bell icon.
Kinds of Quadrilaterals
Trapezium
Trapezium is a quadrilateral with a pair of parallel sides.
Kite
Kite is a special type of a quadrilateral. The sides with the same markings in each figure are equal. For exampleAB =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.
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
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
Property: The diagonals of a parallelogram bisect each other (at the point of their intersection, of course!)
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.
Example 6: In Fig 3.31 HELP is a parallelogram. (Lengths are in cms). Given that OE = 4 and HL is 5 more than PE? Find OH.
Angles of a parallelogram
We studied a property of parallelograms concerning the (opposite) sides. What can we say about the angles?
EXERCISE 3.3
1. Given a parallelogram ABCD. Complete each statement along with the definition or property used. (i) AD = ...... (ii) angle DCB = ...... (iii) OC = ...... (iv) measure of angle DAB + measure of angle CDA = ......
2. Consider the following parallelograms. Find the values of the unknowns x, y, z.
3. Can a quadrilateral ABCD be a parallelogram if (i) angle D + angle B = 180° (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm? (iii) angle A = 70° and angle 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.
7. The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.
8. The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm). In the above figure both RISK and CLUE are parallelograms. Find the value of x.
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 meaure of angle C in Fig 3.33 if AB is parallel to DC.
12. Find the measure of angle P and angle S if SP is parallel to RQ in Fig 3.34. (If you find measure of angle R, is there more than one method to find measure of angleP?)
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