Introduction to Quadrilateral

Q.

$ABCD$ is a parallelogram.

Show that $2DC-DB=AC$.

Q. Angles of a quadrilateral are in the ratio 1:2:3:3. Find the measure of smallest angle of the quadrilateral.

1. ${40}^{\circ }$
2. ${60}^{\circ }$
3. ${120}^{\circ }$
4. None of the above

Q. Show that the bisectors of angles of a parallelogram forma rectangle

Q.

If in a quadrilateral $ABCD$, $AB=BC$ and $CD=DA$, then the figure is a kite.

1. True

2. False

Q. The three angles of a quadrilateral are ${54}^{\circ },{76}^{\circ }$ and ${108}^{\circ }$. Find the value of fourth angle.

1. ${116}^{\circ }$
2. ${118}^{\circ }$
3. ${120}^{\circ }$
4. ${122}^{\circ }$

Q. Find the sum of the exterior angles of a regular polygon of 15 sides.

1. 24 degrees
2. 156 degrees
3. 360 degrees
4. 280 degrees

Q. The sum of interior angles of a quadrilateral is.

1. ${360}^{\circ }$
2. ${180}^{\circ }$
3. ${90}^{\circ }$
4. ${270}^{\circ }$

Q.

The angles of a quadrilateral are in the ratio 3:4:5:6. Find the angles of the quadrilateral.

1. ${60}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$, ${120}^{\circ }$

2. ${30}^{\circ }$, ${40}^{\circ }$, ${50}^{\circ }$, ${60}^{\circ }$

3. ${40}^{\circ }$, ${100}^{\circ }$, ${80}^{\circ }$, ${140}^{\circ }$

4. ${10}^{\circ }$, ${20}^{\circ }$, ${30}^{\circ }$, ${40}^{\circ }$

Q. Square ABPQ and ADRS are drawn on the sides AB and AD of a parallelogram ABCD. Which of the following options is correct?

1. $\angle SAQ=\angle ABC$
2. $\angle SAD=\angle ABC$
3. $\angle SAQ=\angle DAB$
4. $\angle SRD=\angle ADC$

Q. Given below is a parallelogram ABCD. Find the value of x and y.

1. 2 cm, 4 cm
2. 4 cm, 6 cm
3. 1 cm, 2 cm
4. 3 cm, 4 cm

Q.

In a quadrilateral ABCD, $\angle A={90}^{\circ }$, $\angle B=3x$, $\angle C=3x+5$, $\angle D=8x-15$.
Then, the value of $\angle D$ is

1. ${65}^{\circ }$

2. ${60}^{\circ }$

3. ${20}^{\circ }$

4. ${145}^{\circ }$

Q. Given figure, HOPE is a parallelogram. Find the measure of the angles x, y and z.

1. 110${}^{\circ }$, 40${}^{\circ }$ and 30${}^{\circ }$
2. 30${}^{\circ }$, 40${}^{\circ }$ and 60 ${}^{\circ }$
3. 90${}^{\circ }$, 70${}^{\circ }$ and 80${}^{\circ }$
4. 80${}^{\circ }$, 20${}^{\circ }$ and 60${}^{\circ }$

Q. Consider a parallelogram ABCD with diagonals AC = 12 cm and BD = 16 cm. What is the length of AD if the perimeter of triangle AOD is 25 cm?

1. 11 cm
2. 14 cm
3. 12 cm
4. 13 cm

Q. The sum of all the angles of a quadrilateral is equal to ___ .

1. ${180}^{\circ }$
2. ${360}^{\circ }$
3. ${540}^{\circ }$
4. ${720}^{\circ }$

Q.

The angles of a quadrilateral are in the ratio 1:2:5:7. The angles of the quadrilateral are:

1. 40°, 100°, 80°, 140°

2. 60°, 80°, 100°, 120°

3. 10°, 20°, 30°, 40°

4. 30°, 40°, 50°, 60°

Q. ABCD is a rhombus. Length of the diagonal BD is half the length of AB. The perimeter of rhombus ABCD is 80 cm. Find the length of BO.

1. 10 cm
2. 15 cm
3. 20 cm
4. 5 cm

Q. Prove that the four triangles formed by joining in pairs the mid-points of the sides C of a triangle are congruent to each other. [4 marks]

Q. In a quadrilateral ABCD, $\angle A={30}^{\circ },\angle B={150}^{\circ },\angle C={30}^{\circ }\text{and}$ $\angle D={150}^{\circ }$
Then ABCD is a

1. Rectangle
2. Trapezium
3. Kite
4. Parallelogram

Q.

Draw a rough sketch of the polygon of $8$ sides and write its name.

Q. In the following parallelogram, find the value of $x$.

1. 44°
2. 22°
3. 33°
4. 11°

Q.

How many sides an octagon has ?

Q.

Statement 1: Sum of the interior angles of a quadrilateral is ${360}^{\circ }$.

Statement 2: A diagonal divides the quadrilateral into two triangles. The sum of angles of a triangle is ${180}^{\circ }$.

1. Both statements are correct and statement 2 has sufficient information to prove statement 1.

2. Both statements are correct but statement 2 doesn’t have sufficient information to prove statement 1.

3. Statement 1 is correct and statement 2 wrong.

4. Both statements are wrong.

Q.

Which of the following options represents diagonal(s) of the given quadrilateral?

1. BD only

2. AD and DC

3. AB and BC

4. BD and AC

Q. The angles of a quadrilateral $PQRS$, $\angle P,\angle Q,\angle Rand\angle S$ are $x°,(x-10)°,(x+30)°and2x°$
respectively. Sort the angles in increasing order of magnitude.

1. $\angle Q$
2. $\angle P$
3. $\angle R$
4. $\angle S$

Q. Angles of a quadrilateral are $(4x{)}^{\circ },5(x+2{)}^{\circ },(7x-20{)}^{\circ }$ and $6(x+3{)}^{\circ }$. Find the smallest angle of the quadrilateral.

1. ${90}^{\circ }$
2. ${64}^{\circ }$
3. ${114}^{\circ }$
4. ${78}^{\circ }$

Q. Which of the following is not a quadrilateral?

1. Square
2. Circle
3. Rhombus
4. Trapezium

Q.

Three angles of a quadrilateral are ${75}^{\circ }$, ${100}^{\circ }$ and ${55}^{\circ }$. The fourth angle is:

1. 120

2. 130

3. 200

4. 230

Q.

A quadrilateral has

1. two diagonals

2. three diagonals

3. four diagonals

4. none of these

Q.
In the given figure, sides AB and CD of the quadrilateral ABCD are produced. Find the value of $x$.

1. ${70}^{\circ }$
2. ${65}^{\circ }$
3. ${80}^{\circ }$
4. ${75}^{\circ }$

Q. Identify the diagonals of the given quadrilateral.

1. $AD\&BD$
2. $AC\&BD$
3. $AC\&CD$
4. $AC\&BO$