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Standard VII

Mathematics

Definition of Parallel Lines

The given fig...

Question

The given figure shows a trapezium $A B C D$ in which $A B$ is parallel to $D C$ and $A D = B C$ . $∠ D A B = x ∠ C B A$ .Find $x$

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Solution

Draw $D M ⊥ A B$ and $C N ⊥ A B$
$Δ D A M \equiv Δ C B N$ by R.H.S.
$∴ ∠ D A B = ∠ C B A$
$∴ x = 1$

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State true or false:

The following figure shows a trapezium

A B C D

in which

A B

is parallel to

D C

and

A D = B C

, then

∠ D A B = ∠ C B A

The following figure shows a trapezium

A B C D

in which

A B

is parallel to

D C

and

A D = B C

Prove that :

i) ∠ D A B = ∠ C B A

i i) ∠ A D C = ∠ B C D

i i i) A C = B D

i v) O A = O B

and

O C = O D

Q. In the given figure, ABCD is a trapezium in which AB = 7 cm, AD = BC = 5 cm, DC = x cm, and distance between AB and DC is 4 cm. Find the value of x and area of trapezium ABCD.

Q. In the given figure,

A B C D

is a trapezium where

A B | | D C

and

A D = B C

. If

∠ C B A = 82 °

, then the measure of

∠ A D C

is equal to

IN the figure, ABCD is a trapezium in Which AB = 7 cm, AD = BC = 5 cm, DC = x cm, and distance between AB and DC is 4 cm.
Find the value fo x and area of trapezium ABCD.

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The given figure shows a trapezium ABCD in which AB is parallel to DC and AD=BC. ∠DAB=x∠CBA.Find x

Draw DM⊥AB and CN⊥ABΔDAM≡ΔCBN by R.H.S.∴∠DAB=∠CBA∴x=1

The given figure shows a trapezium $A B C D$ in which $A B$ is parallel to $D C$ and $A D = B C$ . $∠ D A B = x ∠ C B A$ .Find $x$

Draw $D M ⊥ A B$ and $C N ⊥ A B$
$Δ D A M \equiv Δ C B N$ by R.H.S.
$∴ ∠ D A B = ∠ C B A$
$∴ x = 1$