Division of a line segment

Q.

What is the ratio $\frac{AC}{BC}$ for the line segment AB following the construction method below?
Step 1. A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at $A_1,A_2,...,A_{30}$
Step 2. A line is drawn from $A_{30}$ to $B$ and a line parallel to $A_{30}B$ is drawn, passing through the point $A_{17}$ and meet AB at C.

1. 17:30

2. 17:13

3. 13:17

4. 13:30

Q. Steps to divide a line segment AB in the given ratio m : n by drawing alternated angles is given. Choose the correct order.
1.Draw any ray AX making acute angle with AB and ray BY such that $\angle BAX=\angle ABY$.
2.Locate the points $A_1,A_2,A_3...A_m$ on AX and $B_1,B_2,B_3...B_n$ on BY such that $A{A}_1=A_1{A}_2=B{B}_1=B_1{B}_2$
3.Draw a ray BY parallel to AX by making $\angle ABY=\angle BAX$
4.Join $A_m{B}_n$.

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

Q.

Which similarity is used to prove that the constructed triangles are similar?

1. SAS Similarity

2. AA Similarity

3. SSS Similarity

4. ASA Similarity

Q.
Number of points to be marked on ray AX which makes an acute angle with AB in order to divide AB into 8cm and 4cm is:

1. 8
2. 4
3. 3
4. 12

Q.

Mention the proper order of identifying a point D on BC such that $\frac{BD}{DC}=\frac{2}{3}$.
1) Join $B_{5}C$ and draw a line parallel to $B_{5}C$ from $B_2$.
2) Identify the ratio in which the point D divides BC using the relation given.
3) Mark 5 points B₁, B₂, B₃, B₄ and B₅ on BX such that they are equidistant.
4) Construct a ray BX which makes an acute angle with line segment BC.
5) The point of intersection of the parallel line from B₂ with BC is the point D.

1. 2, 4, 3, 1, 5

2. 1, 2, 4, 3, 5

3. 3, 5, 2, 4, 1

4. 4, 3, 2, 5, 1

Q.

State whether true or false:
At least 2 rays need to be constructed to divide a line segment into a given ratio

1. False

2. True

Q.

State whether true or false:
To divide a line segment, the constructed ray must be at an obtuse angle to the line segment.

1. True

2. False

Q.

Try to construct triangles using match sticks. Can you make a triangle with $ 3$ matchsticks ?

(Remember you have to use all the available matchsticks in eachcase). If you cannot make a triangle, think of reasons for it.

\( \nabla_{\Delta} \nabla \)

Q. If CR : RS = 2 : 3 and RS : SD = 5 : 6, then S divides line segment CD in the ratio .

1. 5 : 8
2. 18 : 24
3. 25 : 18
4. 5 : 12

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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