NCERT Exemplar Mathematics - Class 9>Chapter 8 - Quadrilaterals>Exercise>Q 1

MEDIUM

9th CBSE

IMPORTANT

Earn 100

A square is inscribed in an isosceles right triangle so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.

Important Questions on Quadrilaterals

MEDIUM

9th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 9>Chapter 8 - Quadrilaterals>Exercise>Q 2

In a parallelogram

A B C D, A B = 10 cm

and

AD = 6 cm

. The bisector of

∠ A

meets

D C

in

E

. If

A E

and

B C

produced meet at

F

, the length of

C F

is

k cm

, then find the value of

k .

MEDIUM

9th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 9>Chapter 8 - Quadrilaterals>Exercise>Q 3

P, Q, R

and

S

are respectively the midpoints of the sides

AB, BC, CD

and

DA

of a quadrilateral

ABCD

in which

AC = BD

. Prove that

PQRS

is a rhombus.

HARD

9th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 9>Chapter 8 - Quadrilaterals>Exercise>Q 4

P, Q, R

and

S

are respectively the midpoints of the sides

AB, BC, CD

and

D A

of a quadrilateral

A B C D

such that

AC ⊥ BD

. Prove that

P Q R S

is a rectangle.

MEDIUM

9th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 9>Chapter 8 - Quadrilaterals>Exercise>Q 5

P, Q, R

and

S

are respectively the midpoints of sides

AB, BC, CD

and

DA

of quadrilateral

ABCD

in which

AC = BD

and

AC ⊥ BD

. Prove that

PQRS

is a square.

EASY

9th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 9>Chapter 8 - Quadrilaterals>Exercise>Q 6

A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

HARD

9th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 9>Chapter 8 - Quadrilaterals>Exercise>Q 7

P

and

Q

are the midpoints of the opposite sides

A B

and

C D

of a parallelogram

A B C D

.

A Q

intersects

D P

at

S

and

B Q

intersects

C P

at

R

. Show that

P Q R S

is a parallelogram.

HARD

9th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 9>Chapter 8 - Quadrilaterals>Exercise>Q 8

A B C D

is a quadrilateral in which

A B ∥ D C

and

A D = B C

. Prove that

∠ A = ∠ B

and

∠ C = ∠ D

.

MEDIUM

9th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 9>Chapter 8 - Quadrilaterals>Exercise>Q 9

In the given figure,

A B ‖ D E, A B = D E, A C ‖ D F

and

A C = D F

. Prove that

BC ‖ EF

and

BC = EF

.