Division of a Line Segment

Q.

Construct a line segment of 10 cm. Divide this line segment in the ratio 3:2. [2 MARKS]

Q. Question 1
Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.

Q. Question 184
In the following figure, $FD\parallel BC\parallel AE$ and $AC\parallel ED$. Find the value of x.

Q. Question 51
To construct a unique parallelogram, the minimum number of measurements required is
a) 2
b) 3
c) 4
d) 5

Q. Which of the following cannot be criteria for the similarity of triangles?

1. Side, Angle, Side
2. Side, Angle, Angle
3. Angle, Angle
4. Side, Side

Q.

(i) Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5.

(ii) Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8 Measure the two parts.

Q.

Construct a line segment of 6 cm. Divide this line segment in the ratio 3:2. [2 MARKS]

Q.

Divide the line segment of 8 cm length in the ratio 4 : 3. Write down the steps to divide a line segment. [2 MARKS]

Q. Steps to divide a line segment AB in the given ratio 3 : 2 by corresponding angles method is given. Choose the correct order.

1. Draw any ray AX making an acute angle with AB
2.Locate 5 points$A_1,A_2,A_3....A_5$ on ray AX
3. Join $B{A}_5$
4.Draw a line parallel to $B{A}_5$ through $A_3$ to AB.

1. 1, 2, 3, 4
2. 2, 1, 3, 4
3. 1, 3, 2, 4
4. 2, 3, 1, 4

Q. Question 3
To divide a line segment AB in the ratio 5:6, draw AX such that $\angle$ BAX is an acute angle, the draw a ray by parallel to AX and the points $A_1,A_2,A_3...$ and $B_1,B_2,B_3...$ are located to equal distances on ray AX and BY, respectively. Then, the points joined are
(A) $A_5$ and $B_6$
(B) $A_6$ and $B_5$​​​​​​​
(C) $A_4$ and $B_5$​​​​​​​
(D) $A_5$ and $B_4$​​​​​​​

Q.

Draw a line segment $AB$ of length $7cm$. Using ruler and compasses, find a point P on AB such that $\frac{AP}{AB}=\frac{3}{5}.$

Q. Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also, justify your construction.

Q.

A point O in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D. Prove that: ${OA}^2+{OC}^2={OB}^2+{OD}^2$. [4 MARKS]

Q. Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.

Q.

Constructing a single ray, divide a line segment of length 12 cm in the ratio 6:3.

Q.

In the given figure ∠ABC=∠BDC=90^o each. Choose the correct similarity from the given choices.

1. ∆ABC~∆BCD

2. ∆ABC~∆CBD

3. ∆ABC~∆DCB

4. ∆ABC~∆BDC

Q. To divide a line segment PQ in the ratio 4 : 5, first a ray PX is drawn so that $\angle QPX$ is an acute angle and then at equal distances points are marked on the ray PX such that minimum number of these points is

1. 4
2. 5
3. 9
4. 11

Q. Image of the division of line segment AB in the ratio 3:2 is given below.

$\angle BAX$ is a/an :

1. acute angle
2. right angle
3. obtuse angle
4. reflex angle

Q. Determine a point which divides a line segment of length 12 cm internally in the ratio 2 : 3 Also, justify your construction.

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.

Draw any line segment $PQ$ without measuring $PQ$ construct a copy of $PQ$.

Q.

Find the value of $\sqrt{4}$ using geometric method.

1. 1

2. 2

3. 2.1

4. 2.9

Q.

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

1. 2:3

2. 6:5

3. 4:9

4. 4:5

Q.

In the figure given below, all the four sides are equal. The construction of which figure is shown in the diagram?

1. Trapezium

2. Rhombus

3. Rectangle

4. Kite

Q.

Step 2. Draw an arc with radius r and B as centre on the first arc at C. So, $\angle COA$ is __.
Note: Answer in degrees.

Q. A triangle ABC with sides BC =7cm, $\angle B={45}^{\circ },\angle A={105}^{\circ }$ is given. The image of constructing a similar triangle of $\Delta ABC$ whose sides are $\frac{3}{4}$ times the corresponding sides of the $\Delta ABC$ is given below. Arrange the steps of construction in the correct order.

1.Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.

2.Join $B_{4}C$ and raw a line through $B_3$( the third point, 3 being smaller of 4 in$\frac{3}{4}$) parallel to $B_{4}C$ to intersect BC at C'.

3.Draw a line through C' parallel to the line CA to intersect BA at A'.

4.Locate 4(the greater of 3 and 4 in$\frac{3}{4}$) points $B_1,B_2,B_3\text{and}{B}_4$ on BX so that $B{B}_1=B_1{B}_2=B_2{B}_3=B_3{B}_4$

1. 1, 3, 2, 4
2. 1, 4, 2, 3
3. 2, 1, 3, 4
4. 2, 3, 1, 4

Q.

Find the value of $\sqrt{20}$ using geometric method.

1. 3

2. 3.9

3. 4.5

4. 5.1

Q. How to visualize a section formula through area. Because I do not able to understand in byju's tablet clearly.

Q.

In the process of construction of ${45}^{\circ }$, what is the sum of all the other angles you would be constructing during the course?

Q. Graphically, the pair of equations $6x-3y+10=0,2x-y+9=0$ represents two lines which are

1. Intersecting at exactly two points
2. Intersecting at exactly one point
3. Coincident
4. Parallel