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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 $A_{5} B .$

Suggest Corrections

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?

The postulate used in the division of line segment to draw

A_{3} C

parallel to

A_{5} B

is :

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. A triangle ABC with sides BC =7cm,

∠ B = 45^{\circ}, ∠ A = 105^{\circ}

is given. The image of constructing a similar triangle of

Δ A B C

whose sides are

\frac{3}{4}

times the corresponding sides of the

Δ A B C

is given below.

The condition used to draw A'C' parallel to AC:

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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 $A_{5} B .$