NCERT Class 8 Mathematics Solutions: Chapter 3 –Understanding Quadrilaterals Exercise 3.4 Part 2

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Given, the figure of convex and concave quadrilateral

A Figure Convex and Concave Quadrilateral

Loading Image

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:

ABC is a Right-Angle Triangle and O is the Mid-Point

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.