Division of a Line Segment

Q.

The number of triangles that can be formed by $5$ points in a line and $3$ points on a parallel line is?

1. ${}^{8}C_3$

2. ${}^{8}C_3–{}^{5}C_3$

3. ${}^{8}C_3–{}^{5}C_3-1$

4. None of these

Q. If ∠𝑂𝐴𝐵 = 40° and 𝐴𝐵 = 𝐶𝐷, then find the measure of ∠𝐶𝑂𝐷.

Q. Question 2
In the given figure, If $AB||CD,CD||EF$ and $y:z=3:7$, find x.

Q.

Draw a line segment AB and by ruler and compasses, obtain a line segment of length $\frac{3}{4}\left(AB\right)$.

Q. Question 1
In the given figure A, B and C are three points on a circle with centre O such that $\angle BOC={30}^{\circ }$ and $\angle AOB={60}^{\circ }$. If D is a point on the circle other than the arc ABC, find $\angle ADC$.

Q.

Consider an acute angled ΔABC. D is any point on the side BC such that $\frac{ar\left(△ABD\right)}{ar\left(△ADC\right)}$ = $\frac{2}{3}$. How would you proceed to construct this line segment AD?

1. Draw a ray BX which makes an acute angle with side BC.

2. Construct triangle ABD such that

3. Draw the median of the

4. Construct triangle ADC such that

Q.

A point $C$ divides a line segment $AB$ in the ratio $5:6$. The ratio of lengths $AB:BC$ is ______.

1. $5:11$

2. $6:11$

3. $11:5$

4. $11:6$

Q.

State whether true or false:
The line segment AB can be divided in a ratio only if the given ratio is less than 1.

1. True

2. False

Q. Question 16
In figure, $\angle ACB={40}^{\circ }$. Find $\angle OAB$.

Q. Question 5
In the figure, BA || ED and BC || EF. Show that $\angle ABC=\angle DEF$.

Q. In the given figure AP : PB = 20 : 6 ,
then what's the value of x?

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

Q.

The point C divides the line segment AB in the ratio 3:7. Find the length of AB (in cm) if the line segment BC is 3.5 cm long -

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Q. $p:$ Every square is a rectangle.
$q:$ Every rhombus is a kite.

1. F, F
2. F, T
3. T, F
4. T, T

Q. Construct a cyclic quadrilateral ABCD in which AB$=6$cm, AC$=7$cm, BC$=6$cm, and AD$=4.2$cm.

Q. Question 5
Construct the following and give justification :​​​​​​​
​​​​​​​
A rhombus whose diagonals are 4cm and 6cm in lengths.

Q.

What is the number of arcs that need to be drawn during the construction of 60 degree angle?__

Q. In fig if $AB$ $\parallel$ $DE$, $\angle BAC={35}^{\circ }$ and $\angle CDE={53}^{\circ }$, find $\angle DCE$ in degrees.

Q.

The number of divisions required to divide a line segment in the ratio 10:11 using a single ray is: ___

Q. Construct each of the following angles, using ruler and compasses:
${105}^o$

Q.

A line segment AB is divided in the ratio 4:9 by a point C. Find the length AC (in cm) if AB=26 cm.

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Q. Construct each of the following angles, using ruler and compasses:
${75}^o$

Q.

The following steps illustrate the formation of a perpendicular bisector.

1. True

2. False

Q.

If a line segment AB is divided in the ratio m : n, both m and n are

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integers.

Q.

What is the number of arcs that need to be drawn during the construction of 60 degree angle?__