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

Byju's Answer

Standard IX

Mathematics

The Mid-Point Theorem

ABCD is a qua...

Question

ABCD is a quadrilateral in which AB || DC and AD || BC. A line MN, parallel to CD, is drawn meets the midpoint M of the side BC which meets AD at N. What can you say about the diagonal AC?

Line AC is twice the length AD.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Line MN bisects AC.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Line AC is $\frac{1}{3}$ rd the length MN.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of the above.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
Line MN bisects AC.

Since AB, CD and MN are all parallel lines, we can think of AD, AC and BC as transversals on the parallel lines.
$∴$ By equal intercept theorem, AN = ND and AO = OC.
$\Rightarrow$ Line MN bisects diagonal AC.

Suggest Corrections

Similar questions

Q. In quadrilateral ABCD, AC = AD and AB bisects

∠

A. Show that

△ A B C ≅ △ A B D

. What can you say about BC and BD ?

Q. In quadrilateral ABCD, prove that
(i)

¯ ¯¯¯¯¯¯ ¯ A B + ¯ ¯¯¯¯¯¯ ¯ B C + ¯ ¯¯¯¯¯¯¯ ¯ A D + ¯ ¯¯¯¯¯¯¯ ¯ D C = 2 ¯ ¯¯¯¯¯¯ ¯ A C

(ii)

¯ ¯¯¯¯¯¯¯ ¯ A D + ¯ ¯¯¯¯¯¯ ¯ B C = 2 ¯ ¯¯¯¯¯¯¯¯¯ ¯ M N

, where M and N are the mid points of side AB and CD respectively.

A B C D

is a trapezium in which

A B ∥ D C

M

and

N

are the midpoints of

A D

and

B C

respectively. If

A B = 12 c m; M N = 14 c m

find

C D

State true or false:

In triangle

A B C

D

and

E

are points on side

A B

such that

A D = D E = E B

. Through

D

and

E

lines are drawn parallel to

B C

which meet side

A C

at points

F

and

G

respectively. Through

F

and

G

lines are drawn parallel to

A B

which meet side

B C

at points

M

and

N

respectively, then

B M = M N = N C

In quadrilateral $A C B D, A C = A D$ and $A B$ bisects $∠ A$ . Show that $△ A B C ≅ △ A B D$ . What can you say about $B C$ and $B D$ ?

Join BYJU'S Learning Program

ABCD is a quadrilateral in which AB || DC and AD || BC. A line MN, parallel to CD, is drawn meets the midpoint M of the side BC which meets AD at N. What can you say about the diagonal AC?

The correct option is B Line MN bisects AC. Since AB, CD and MN are all parallel lines, we can think of AD, AC and BC as transversals on the parallel lines. ∴ By equal intercept theorem, AN = ND and AO = OC. ⇒ Line MN bisects diagonal AC.

The correct option is B
Line MN bisects AC.

Since AB, CD and MN are all parallel lines, we can think of AD, AC and BC as transversals on the parallel lines.
$∴$ By equal intercept theorem, AN = ND and AO = OC.
$\Rightarrow$ Line MN bisects diagonal AC.