Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.4>Q 7

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IMPORTANT

Earn 100

$A B C$ is a triangle. The bisector of the exterior angle at $B$ and the bisector of $∠ C$ intersect each other at $D$ . Prove $∠ B D C = \frac{1}{2} ∠ A$ .

Important Questions on Lines and Angles

HARD

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.2>Q 5

From a point

O

in a line

A B,

ray

O C

and

O D

are drawn on opposite sides of

A B

such that

∠ B O C = ∠ A O D

. Prove that

O C

and

O D

are opposite rays.

HARD

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IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.3>Q 7

Prove that if two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.

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IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.4>Q 8

In a

∆ A B C, A D

bisects

∠ A and ∠ C > ∠ B

. Prove that

∠ A D B > ∠ A D C

.

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IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.4>Q 9

The side

B C

of a

∆ A B C

is produces to

D

to form the exterior angle

∠ A C D

. The bisector of

∠ B A C

at

B C at E

. Prove that

∠ A B C + ∠ A C D = 2 ∠ A E C

.

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9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.4>Q 10

A B C

is an isosceles triangle in which

A B = A C

and

A E

bisects the exterior angle

C A D at A

. Prove that

A E ∥ B C

.