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Standard X

Mathematics

Division of a Line Segment

In the given ...

Question

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?

Corresponding angle are equal

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Alternate interior angles are equal

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Co-interior angle are supplementary

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Perpendicular bisector theorem

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Solution

The correct option is B Alternate interior angles are equal

Here we use alternate interior angles are equal then the lin4es are parallel and $∠ X A B = ∠ A B Y$ as AX parallel to BY.

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Similar questions

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. 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

∠ B A X = ∠ A B Y

.
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

∠ A B Y = ∠ B A X

4.Join

A_{m} B_{n}

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

∠ B A X = ∠ A B Y

.
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

∠ A B Y = ∠ B A X

4.Join

A_{m} B_{n}

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.

Q. To divide a line segment

A B

in the ratio

5 : 6

, draw a ray

A X

such that

∠

B A X

is an acute angle, then draw a ray

B Y

parallel to

A X

and the points

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

... and

B_{1}, B_{2}, B_{3},

... are located at equal distances on ray

A X

and

B Y

, respectively. Then the points joined are ____

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The correct option is B Alternate interior angles are equal Here we use alternate interior angles are equal then the lin4es are parallel and ∠XAB=∠ABY as AX parallel to BY.

The correct option is B Alternate interior angles are equal

Here we use alternate interior angles are equal then the lin4es are parallel and $∠ X A B = ∠ A B Y$ as AX parallel to BY.