Types of Quadrilaterals

Q.

What is the difference between convex and concave polygons?

Q.

Are diagonals of a rhombus equal?

Q.

1)A polygon has 27 diagonals. How many sides does it have?

Q.

Name the quadrilateral whose diagonals are equal and bisect each other at right angles

Q.

The polygon in which sum of all exterior angles is equal to the sum of interior angles is called __________.

Q.

Fill in the blanks :
(i) A quadrilateral has ___ sides.
(ii) A quadrilateral has ___ angles.
(iii) A quadrilateral has ___ vertices, no three of which are ___.
(iv) A quadrilateral has ___ diagonals.
(v) A diagonal of a quadrilateral is a line segment that joins two ___ vertices of the quadrilateral.
(vi) The sum of the angles of a quadrilateral is ___.

Q.

Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.

Q.

Square is a regular quadrilateral.

1. False

2. True

Q.

Which of the following is/are concave quadrilaterals?

1. II & IV

2. IV

3. II

4. I & III

Q.

In the figure, ABCD is a quadrilateral.
(i) Name a pair of adjacent sides.
(ii) Name a pair of opposite sides.
(iii) How many pairs of adjacent sides are there?
(iv) How many pairs of opposite sides are there?

(v)Name a pair of adjacent angles.
(vi) Name a pair of opposite angles.
(vii) How many pairs of adjacent angles are there?
(viii) How many pairs of opposite angles are there?

Q.

The total number of parallelograms in this figure is

___

Q.

Which of the following quadrilaterals has equal length of diagonals?

i)Rhombus

ii) Rectangle

iii) Square

iv) Kite

v) Parallelogram

1. ii, iii, iv

2. i, ii, iii

3. ii, iii

4. ii, iii, v

Q.

Define the following terms:
(i) Quadrilateral (ii) Convex Quadrilateral.

Q. If a part of the line connecting two interior points that lie outside the polygon, then it is called ________.

1. concave polygon
2. convex polygon
3. regular polygon
4. irregular polygon

Q.

How many diagonals does each of the following have?

(a) A convex quadrilateral

(b) A regular hexagon

(c) A triangle

Q. Match the following with the values of 'x'.

1. 125°
2. 48°
3. 145°

Q.

Suppose ABC is an equiangular triangle. Prove that it is equilateral. (You have seen earlier that an equilateral triangle is equiangular. Thus for triangles equiangularity is equivalent to equilaterality.)

Q. The following figure is an example of ______.

1. concave polygon
2. convex polygon
3. regular polygon
4. irregular polygon

Q.

The measure of atleast one angle of a concave quadrilateral is __________ $180°$

Q.

When we start constructing a quadrilateral with 2 diagonals and 3 sides known, in how many ways can the construction be started?

1. 2

2. 3

3. 4

4. 1

Q. Question 78
Fill in the blanks to make the statements true.
The measure of ___ angle of a concave quadrilateral is more than ${180}^{\circ }$.

Q.

Diagonals in following quadrilateral are equal or

I) parallelogram. 2) rhombus 3) rectangle 4) trapezium

Q. Fill in the blanks.
For a convex polygon of n sides, we have:
(i) Sum of all exterior angles = .........
(ii) Sum of all interior angles = .........
(iii) Number of diagonals = .........

Q. How many diagonals does each of the following have?
(1.) A convex Quadrilateral
Find the answer of this question?

Q. If the lengths of three sides of an isosceles trapezium are 10 cm, 5 cm and 4 cm, its perimeter CANNOT be

1. 23 cm
2. 25 cm
3. 29 cm
4. 31 cm

Q. Which of the following statements are incorrect?

1. Three non-collinear points form a triangle.
2. No three vertices of a quadrilateral are collinear.
3. Any two vertices of a quadrilateral are non - collinear.
4. Four non - collinear points form a quadrilateral.

Q.

The sum of the four angles of a quadrilateral is $360°$

The angle of a quadrilateral are respectively $100°,98°,92°.$ The measure of fourth angle is:

1. $70°$

2. $290°$

3. $98°$

4. $92°$

Q. Identify the number of concave polygons from the given figures?

1. $1$
2. $2$
3. $3$
4. $4$

Q.

There is a pair of parallel lines which intersects with another pair of parallel lines. The quadrilateral formed is trapezium.

1. True

2. False

Q. Which of the following statements are incorrect?

1. Three collinear points form a triangle.
2. No three vertices of a quadrilateral are collinear.
3. Any two vertices of a quadrilateral are non - collinear.
4. Four non - collinear points form a quadrilateral.