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Standard X

Mathematics

Basic Proportionality Theorem

In the adjoin...

Question

In the adjoining figure ABCD is a parallelogram. ‘P’ is a point on BC, DP and AB are produced meet at L. Prove that DP : PL = DC : BL.

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Solution

ABCD is a parallelogram.

In ΔALD, PB || AD.

By Basic Proportionality Theorem, we have:

We know that the opposite sides of a parallelogram are equal.

∴ AB = CD … (2)

From (1) and (2), we have:

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Similar questions

Q. ABCD is a parallelogram, P is a point on side BC such that DP produced meets AB produced at L.. Prove that

(i)

\frac{D P}{P L} = \frac{D C}{B L}

(ii)

\frac{D L}{D P} = \frac{A L}{D C}

$P$ is a point on side $B C$ of a parallelogram $A B C D$ . If $D P$ produced meets $A B$ produced at point $L$ , prove that :
(i) $D P : P L = D C : B L$ .
(ii) $D L : D P = A L : D C$ .

Q. P is a point on side BC of a parallelogram ABCD. If DP produced meet AB produced at point L, then

D P : P L = D C : B L

Q. In the adjoining figure, ABCD is a parallelogram. P is a point on BC such that BP

:

= 1 : 2

. DP produced meets AB produced at Q. Given ar(

Δ

CPQ)

= 20 c m^{2}

. Calculate ar(

Δ

CDP).

Q. In the adjoining figure,

A B C D

is a parallelogram.

P

is a point on

B C

such that

B P : P C = 1 : 2

and

D P

produced meets

A B

produced at

Q

. If area of

△ C P Q = 20 c m^{2}

, find
(i) area of

△ B P Q

.
(ii) area

△ C D P

.
(iii) area of parallelogram

A B C D

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In the adjoining figure ABCD is a parallelogram. ‘P’ is a point on BC, DP and AB are produced meet at L. Prove that DP : PL = DC : BL.

ABCD is a parallelogram. In ΔALD, PB || AD. By Basic Proportionality Theorem, we have: We know that the opposite sides of a parallelogram are equal. ∴ AB = CD … (2) From (1) and (2), we have:

ABCD is a parallelogram.

In ΔALD, PB || AD.

By Basic Proportionality Theorem, we have:

We know that the opposite sides of a parallelogram are equal.

∴ AB = CD … (2)

From (1) and (2), we have: