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Standard X

Mathematics

Division of a Line Segment

In the given ...

Question

In the given image, segment $A B$ has been divided in the ratio $3 : 2$ . This is done by
1) Drawing $∠ B A X$
2) marking equal lengths $A A_{1}, A_{1} A_{2}, A_{2} A_{3}, A_{3} A_{4} & A_{4} A_{5}$
3) Point $A_{5}$ is joint to point B
4) $A_{3} C$ is drawn parallel to $A_{5} B$ by using which of the properties of parallel lines?

Corresponding angles are equal

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Alternate interior angles are equal

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Co-interior angles are supplementary

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Perpendicular bisector theorem

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Solution

The correct option is A Corresponding angles are equal

Here we use the principle that when corresponding angles are equal, the lines are parallel.
$∠ A A_{3} C = ∠ A A_{5} C$ as $A_{3} C$ is parallel to $A_{5} B .$

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Similar questions

Q. In the given image, segment

A B

has been divided in the ratio

3 : 2

. This is done by
1) Drawing

∠ B A X

2) marking equal lengths

A A_{1}, A_{1} A_{2}, A_{2} A_{3}, A_{3} A_{4} & A_{4} A_{5}

3) Point

A_{5}

is joint to point B
4)

A_{3} C

is drawn parallel to

A_{5} B

by using which of the properties of parallel lines?

Q. In the given image, segment AB has been divided in the ratio 3:2. This is done by
1. Draw any ray AX making acute angle with AB.
2. Draw a ray BY parallel to AX by making

∠ A B Y = ∠ B A X

3. Locate the points

A_{1}, A_{2}, A_{3} . . . A_{3}

on AX and

B_{1}, B_{2}

on BY such that

A A_{1} = A_{1} A_{2} = B B_{1} = B_{1} B_{2}

4. Join

A_{3} B_{2}

by using which of the properties of parallel lines?

Q. In the given image, segment AB has been divided in the ratio 3:2. This is done by
1. Draw any ray AX making acute angle with AB.
2. Draw a ray BY parallel to AX by making

∠ A B Y = ∠ B A X

3. Locate the points

A_{1}, A_{2}, A_{3} . . . A_{3}

on AX and

B_{1}, B_{2}

on BY such that

A A_{1} = A_{1} A_{2} = B B_{1} = B_{1} B_{2}

4. Join

A_{3} B_{2}

by using which of the properties of parallel lines?

Q. The image of dividing line segment AB of length 12cm into 8cm and 4cm is given below.

Arrange the steps of construction in the correct order.
1. Mark three points on AX such that

A A_{1} = A_{1} A_{2} = A_{2} A_{3}

2.Draw an acute angle

∠ B A X

3.Join

A_{3}

to B.
4.Draw

A_{2} C

parallel to

A_{3} B

The figure given below have been constructed by following the steps given below.

I: Draw line segment AB of length 16.9 cm and draw a ray AX making an acute angle with line segment AB.

II: Mark points Alf A₂, A₃, A₄........A₁₃, on AX such that AA₁ = A₁A₂ = A₂A₃ and

so on.

III: Join BA₁₃. Through the point A₅, draw a line parallel to BA₁₃ intersecting AB at point C.

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In the given image, segment AB has been divided in the ratio 3:2. This is done by 1) Drawing ∠BAX 2) marking equal lengths AA1,A1A2,A2A3,A3A4 & A4A5 3) Point A5 is joint to point B 4) A3C is drawn parallel to A5B by using which of the properties of parallel lines?

The correct option is A Corresponding angles are equal Here we use the principle that when corresponding angles are equal, the lines are parallel. ∠AA3C=∠AA5C as A3C is parallel to A5B.

The correct option is A Corresponding angles are equal

Here we use the principle that when corresponding angles are equal, the lines are parallel.
$∠ A A_{3} C = ∠ A A_{5} C$ as $A_{3} C$ is parallel to $A_{5} B .$