MATHEMATICS>Chapter 7 - Congruent Triangles>EXERCISE 7.1>Q 1

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9th CBSE

IMPORTANT

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If the bisector of the vertical angle of a triangle bisects the base of the triangle, then prove that the triangle is isosceles.

Important Questions on Congruent Triangles

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9th CBSE

IMPORTANT

MATHEMATICS>Chapter 7 - Congruent Triangles>EXERCISE 7.1>Q 2

In figure,

A B C

is a

∆

in which

A B = A C

and

A D

is an altitude on

B C

. Prove that

A D

bisects

∠ A

.

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9th CBSE

IMPORTANT

MATHEMATICS>Chapter 7 - Congruent Triangles>EXERCISE 7.1>Q 3

∆ A B C

is an isosceles triangle with

A B = A C

. Side

B A

is produced to

D

such that

A B = A D

. Prove that

∠ B C D

is a right angle.

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9th CBSE

IMPORTANT

MATHEMATICS>Chapter 7 - Congruent Triangles>EXERCISE 7.1>Q 4

In Figure,

P Q = P R

.

Q M

and

R N

are respectively the bisectors of

∠ Q

and

∠ R

. Prove that

M R = N Q

.

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9th CBSE

IMPORTANT

MATHEMATICS>Chapter 7 - Congruent Triangles>EXERCISE 7.1>Q 5

In Figure,

∠ Q = ∠ R, P Q = P R

and

Q M

and

R N

intersect at

O

. Prove that

∆ P Q M ≅ ∆ P R N

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9th CBSE

IMPORTANT

MATHEMATICS>Chapter 7 - Congruent Triangles>EXERCISE 7.1>Q 6

In figure, $∠ Q = ∠ R$ , $P Q = P R$ and $Q M$ and $R N$ intersects at $O .$ Prove that $P M = P N .$

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9th CBSE

IMPORTANT

MATHEMATICS>Chapter 7 - Congruent Triangles>EXERCISE 7.1>Q 7

In Figure,

A B = B C

and

A D = C E

. Prove that

∠ A B E = ∠ C B D

.

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9th CBSE

IMPORTANT

MATHEMATICS>Chapter 7 - Congruent Triangles>EXERCISE 7.1>Q 8

In Figure,

A D

is a median of

∆ A B C

.

B M

and

C N

are perpendiculars on

A D

and

A D

produced respectively. Prove that

B M = C N .

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MEDIUM

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 7 - Congruent Triangles>EXERCISE 7.1>Q 9

In Figure,

A B C D

is a quadrilateral in which

A B | | C D

and

A B = C D

.

A P

and

C Q

are perpendiculars from

A

and

C

on diagonal

B D

. Prove that

A P = C Q

.

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