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# Mathematics – Class 8 – Chapter 3-Understanding Quadrilaterals – Exercise – 3.4 – NCERT Exercise Solution

1. State whether True or False.

(a) All rectangles are squares.

(b) All rhombuses are parallelograms.

(c) All squares are rhombuses and also rectangles.

(d) All squares are not parallelograms.

(e) All kites are rhombuses.

(f) All rhombuses are kites.

(g) All parallelograms are trapeziums.

(h) All squares are trapeziums.

Solution:

(a) False.

(b) True

(c) True

(d) False.

(e) False.

(f) True

(g) True

(h) True

2. Identify all the quadrilaterals that have.

(a)four sides of equal length

Solution: Rhombus and square

(b) four right angles

Solution: Square and rectangle

3. Explain how a square is.

Solution: Square is a quadrilateral because it has four sides.

(ii) a parallelogram

Solution: Square is a parallelogram because it’s opposite sides are parallel and opposite angles are equal.

(iii) a rhombus

Solution: Square is a rhombus because all the four sides are of equal length and diagonals bisect at right angles.

(iv) a rectangle

Solution: Square is a rectangle because each interior angle, of the square, is 90°. Its opposite sides are equal and has equal diagonal.

4. Name the quadrilaterals whose diagonals.

(i) bisect each other

Solution:  Parallelogram, Square, Rhombus and Rectangle

(ii) are perpendicular bisectors of each other

Solution: Rhombus and Square

(iii) are equal

Solution: Rectangle and Square

5. Explain why a rectangle is a convex quadrilateral.

Solution:

Rectangle is a convex quadrilateral because both of its diagonals lie in it’s interior.

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).

Solution:

Here, AD and DC are drawn so that AD || BC and AB || DC

AD = BC and AB = DC

ABCD is a rectangle,

Thus, opposite sides are equal and parallel to each other and all the interior angles are of 90°.

We know that in a rectangle, diagonals are of equal length and also bisects each other.

Thus, AO = OC = BO = OD

Hence, O is equidistant from A, B and C.

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