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Standard X

Mathematics

Division of a Line Segment

AB is a line ...

Question

AB is a line segment which is inclined to line XY, such that they intersect at point O. A line PQ is drawn which intersects line XY at point P at the same angle of inclination as AB. Line PQ is __ to line segment AB.

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Solution

The angle AB and PQ make with XY are equal. Therefore, by the corresponding angles postulate, the lines AB and PQ are parallel lines.

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Similar questions

AB is a line segment which is inclined to line XY, such that they intersect at point O. A line PQ is drawn which intersects the line XY at point P at the same angle of inclination as AB. Line PQ is _________ to line segment AB.

Q. AB is a line segment AX and BY are two equal line segments drawn opposite sides of line AB such that AX ||BY.
If line segments AB and XY intersect each other at point P. Prove that
(a)

Δ A P X ≅ Δ B P Y

(b) line segments AB and XY bisect each other at P.

A B

is a line segment,

A X

and

B Y

are two equal line segments drawn opposite sides of line

A B

, such that

A X ∥ B Y

. If

Δ A P X ≅ Δ B P Y

then, line segments

A B

and

X Y

intersect each other at point

P

such that:

A line segment AB is bisected at point P and through point P another line segment PQ, which is perpendicular to AB, is drawn. Show that : QA =QB.

State whether the following statement is true or false.

If a line segment

A B

is bisected at point

P

and through point

P

another line segment

P Q

which is perpendicular to

A B,

is drawn then

Q A = Q B .

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