# NCERT Class 8 Mathematics Solutions: Chapter 3 – Understanding Quadrilaterals Exercise 3.4 Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question: 4** Name the quadrilateral whose diagonals.

(I) Bisect each other.

(II) Are perpendicular bisectors of each other?

(III) Are equal.

**Answer**:

(I) If diagonals of a quadrilateral bisect each other then it is a **rhombus, parallelogram, rectangle or square**.

(II) If diagonals of a quadrilateral are perpendicular bisector of each other,

Then it is a **rhombus or square**.

(III) If diagonals are equal, then it is a **square or rectangle**.

**Question: 5** Explain why a rectangle is a convex quadrilateral.

**Answer**:

In a rectangle there are two diagonals, both lying in the interior of the rectangle.

Its vertex is raised and both of its diagonals lie in its interior.

So, it is a convex quadrilateral.

**Question: 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.)

Image:

**Answer**:

Here, two right triangles make a rectangle.

AD and DC are drawn. So, that and

So, and

Where, O is equidistant point from A, B, C and D because O is the mid-point of the two diagonals of a rectangle.

ABCD is rectangle and in rectangle diagonals are of equal length and also bisects each other.

Hence, AO = OC = BO = OD.

So, O is the equidistant from A, B and C.