Скачать или смотреть Understanding Quadrilaterals - Maths Class 8th - Ex 3.4 - Q2 to Q6 - Chapter 3 - NCERT - CBSE

Understanding Quadrilaterals - Maths Class 8th - Ex 3.4 - Question 2 to 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.

Some Special Parallelograms
Rhombus : We obtain a Rhombus (which, you will see, is a parallelogram) as a special case of kite (which is not a a parallelogram). Note that the sides of rhombus are all of same length; this is not the case with the kite. A rhombus is a quadrilateral with sides of equal length. Since the opposite sides of a rhombus have the same length, it is also a parallelogram. So,a rhombus has all the properties of a parallelogram and also that of a kite. The most useful property of a rhombus is that of its diagonals.
Property: The diagonals of a rhombus are perpendicular bisectors of one another.

A rectangle: A rectangle is a parallelogram with equal angles. Thus each angle of a rectangle is a right angle. So, a rectangle is a parallelogram in which every angle is a right angle. Being a parallelogram, the rectangle has opposite sides of equal length and its diagonals bisect each other. In a parallelogram, the diagonals can be of different lengths. (Check this); but surprisingly the rectangle (being a special case) has diagonals of equal length.
Property: The diagonals of a rectangle are of equal length. In a rectangle the diagonals, besides being equal in length bisect each other.

A square: A square is a rectangle with equal sides. This means a square has all the properties of a rectangle with an additional requirement that all the sides have equal length. The square, like the rectangle, has diagonals of equal length. In a rectangle, there is no requirement for the diagonals to be perpendicular to one another In a square the diagonals. (i) bisect one another (square being a parallelogram) (ii) are of equal length (square being a rectangle) and (iii) are perpendicular to one another. Hence, we get the following property.
Property: The diagonals of a square are perpendicular bisectors of each other.

EXERCISE 3.4
1. State whether True or False. (a) All rectangles are squares (e) All kites are rhombuses. (b) All rhombuses are parallelograms (f) All rhombuses are kites. (c) All squares are rhombuses and also rectangles (g) All parallelograms are trapeziums. (d) All squares are not parallelograms. (h) All squares are trapeziums.
2. Identify all the quadrilaterals that have. (a) four sides of equal length (b) four right angles
3. Explain how a square is. (i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle
4. Name the quadrilaterals whose diagonals. (i) bisect each other (ii) are perpendicular bisectors of each other (iii) are equal
5. Explain why a rectangle is a convex quadrilateral.
6. 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 to help you).

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