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Basic Proportionality Theorem and Its Forms

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Through the vertex A of paralle\log ram ABCD ,a line AEF is drawn to meet BC at E And DC produced at F.Show that triangle BEF and DCE are equal in are

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Q. Through the vertex

A

of a parallelogram

A B C D

A E F

is drawn to meet

B C

E

D C

F

. Show that the area

(Δ B E F)

(Δ D C E)

A B C D

is a parallelogram, a line through

A

D C

P

B C

Q

.
Prove that triangle

B C P

is equal in area to triangle

D P Q

.

Q. In a trapezium

A B C D,

A B ∥ D C

L

in the mid-point of

B C .

L,

L M

is drawn parallel to

A D

A B

X

D C

Y .

a r (A B C D) = a r (A X Y D)

Q. In the given figure ,

A B C D

is a quadrilateral.A line through

D

A C

B C

E

(△ A B E) =

area of quadrilateral

A B C D

Q. Question 8
In trapezium ABCD, AB || DC and L is the midpoint of BC. Through L, a line PQ || AD has been drawn which meets AB in P and DC produced in Q. prove that ar (ABCD) = ar (APQD).

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