Dividing Line Segment into Equal Parts

Q.

What is the length of the line segment joining the mid points of the diagonals of a trapezium that is parallel to each of the parallel sides having lengths 12 cm and 4 cm.

1. 2 cm

2. 4 cm

3. 6 cm

4. 3 cm

Q.

In the figure below, two vertices of a parallelogram are joined to the mid points of two sides.

Then, the lines divide the diagonal in the picture into 3 equal parts.

1. False

2. True

Q. Draw a rectangle of perimeter 17 cm and sides in the ratio of 5 : 3. Find the measure of the smallest side.

1. 3.2

Q. In the figure below, two vertices of a parallelogram are joined to the mid points of two sides. Then, the lines divide the diagonal in the picture into _______ equal parts.

1. 3

Q. AB and CD are parallel lines.
Then,

1. $AP\times PC=(BP{)}^2\times (PD{)}^2$
2. $AP\times PC=(BP{)}^2\times PD$
3. $AP\times PC=\frac{BP}{PD}$
4. $AP\times PC=BP\times PD$

Q. In the figure $l||m,n||p$ and $\angle 1={85}^{\circ }$, then $\angle 2$ is equal to.

1. ${66}^{\circ }$
2. ${40}^{\circ }$
3. ${45}^{\circ }$
4. ${95}^{\circ }$

Q. In the given figure, if $l_1$ || $l_2$, what is the value of x°?

1. 75
2. 80
3. 60
4. 85

Q. If AP:PQ = 1:2 and PQ:QB = 4:5, then Q divides line segment AB in the ratio of?

1. 4:5
2. 2:3
3. 6:5
4. 4:9

Q. Draw a rectangle of perimeter 17 cm and sides in the ratio of 5:3. Also, find the measure of the smallest side.

Q. In the given figure find the value of $\angle AOC$.

1. ${130}^{\circ }$
2. ${140}^{\circ }$
3. ${150}^{\circ }$
4. ${160}^{\circ }$

Q.

In the figure, two lines intersect at O. If x = ${75}^{\circ }$, find $\angle$u + $\angle$y.

1. ${315}^{\circ }$

2. ${270}^{\circ }$

3. ${105}^{\circ }$

4. ${210}^{\circ }$

Q. In the given figure, $PQRS$ is a cyclic quadrilateral. Its diagonals $PR$ and $QS$ intersect each other at $T$. If $\angle PRS={80}^{\circ }and\angle RQS={50}^{\circ }$, calculate $\angle PSR$.

1. ${30}^{\circ }$
2. ${50}^{\circ }$
3. ${70}^{\circ }$
4. ${90}^{\circ }$

Q. In the figure, $POQ$ is a diameter abd $OQRS$ is a cyclic quadrilateral. If $\angle PSR={150}^o$, find $\angle RPQ$.

Q. construct a traingle ABC such that BC =6cm AB=6cm and median AD=4cm

Q. Draw a rectangle of perimeter 17 cm and sides in the ratio of 5:3. Also, find the measure of the smallest side.

Q.

In the figure below, two vertices of a parallelogram are joined to the mid points of two sides.

Show that the lines divide the diagonal given into 3 equal parts.

Q.

In a triangle ABC, median AD is produced to X such that AD = DX. Prove that ABXC is a parallelogram. [2 MARKS]

Q. In the given figure, O is the centre of the circle. PQ is a chord of the circle and R is any point on the circle. If $\angle PRQ=l$ and $\angle OPQ=m,$ then $l+m$=___.

1. ${70}^{\circ }$
2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${180}^{\circ }$

Q. $\angle$1 and $\angle$2 form linear pair. If $\angle$1 = 40°, find $\angle$2.

1. 40°
2. 100°
3. 80°
4. 140°

Q. In the given figure, O is the centre of a circle and PQ is a diameter. If $\angle ROS={40}^{\circ },$ then what is the value of $\angle RTS$?

1. ${20}^{\circ }$
2. ${45}^{\circ }$
3. ${70}^{\circ }$
4. ${65}^{\circ }$

Q.

1. ${30}^o$
2. ${60}^o$
3. ${90}^o$
4. ${45}^o$

Q.

In the figure below, two vertices of a parallelogram are joined to the mid points of two sides.

Show that the lines divide the diagonal given into 3 equal parts.