CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Properties of Parallelograms

Question 5 iD...

Question

Question 5 (i)
D, E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC Show that BDEF is a parallelogram.

Open in App

Solution

F ,E are the midpoints of the sides AB and AC respectively.
$∴ F E | | B C a n d F E = \frac{1}{2} B C$
$\Rightarrow F E | | B C a n d F E = B D [D i s m i d p o i n t o f B C] . . . . . (1)$
Similarly; D, E are the midpoints of BC and AC respectively.
$∴ E D | | A B a n d E D = \frac{1}{2} A B$
$\Rightarrow E D | | A B a n d E D = F B [F i s m i d p o i n t o f A B] . . . . . (2)$
From (1) and (2), we can conclude that BDEF is a parallelogram.

Suggest Corrections

thumbs-up

0

Similar questions

D, E

F

are respectively the mid-points of the sides

B C, C A

A B

△ A B C

B D E F

is a parallelogram.

Q. Question 5 (iii)
D, E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC Show that:

(i i i) a r e a (B D E F) = \frac{1}{2} a r e a (A B C)

D, E

F

are respectively the mid-points of the sides

B C, C A

A B

△ A B C

. Show that
(i)

B D E F

is a parallelogram
(ii)

a r (D E F) = \frac{1}{4} a r (A B C)

a r (B D E F) = \frac{1}{2} a r (A B C)

D, E and F are respectively the mid-points of the sides BC, CA and AB of a $△$ ABC. Show that
(i) BDEF is a parallelogram.(ii) ar ( $△$ DEF) = $\frac{1}{4}$ ar ( $△$ ABC). [4 MARKS]

D, E and F are respectively the mid-points of the sides BC, CA and AB of a ΔABC. Show that

(i) BDEF is a parallelogram.

(ii) ar (DEF) = ar (ABC)

(iii) ar (BDEF) = ar (ABC)

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Properties of Parallelograms

Standard VIII Mathematics

Join BYJU'S Learning Program

CrossIcon