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

MEDIUM

9th CBSE

IMPORTANT

Earn 100

$D, E$ and $F$ are the midpoints of the sides $BC, CA$ and $AB$ , respectively of an equilateral triangle $ABC$ . Show that $△ DEF$ is also an equilateral triangle.

Important Questions on Quadrilaterals

MEDIUM

9th CBSE

IMPORTANT

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

Points

P

and

Q

have been taken on opposite sides

AB

and

CD

, respectively of a parallelogram

ABCD

such that

AP = CQ

. Show that

AC

and

PQ

bisect each other.

MEDIUM

9th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 9>Chapter 8 - Quadrilaterals>Exercise>Q 10

In the given figure,

P

is the midpoint of side

BC

of a parallelogram

ABCD

such that

∠ BAP = ∠ DAP

. Prove that

AD = 2 CD

.

MEDIUM

9th CBSE

IMPORTANT

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

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.

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.