MATHEMATICS>Chapter 8 - Quadrilaterals>EXERCISE>Q 15

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9th CBSE

IMPORTANT

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$A B C D$ is a parallelogram, $A E$ and $B F$ are respectively, the perpendiculars from $A$ and $B$ to $D C$ and $D C$ produced. Prove that $A E = B F$ .

Important Questions on Quadrilaterals

EASY

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 8 - Quadrilaterals>EXERCISE>Q 16

A B C D

is a trapezium is which

A B ∥ C D

and

A D = B C

, prove that

∠ A - ∠ B = 0

EASY

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IMPORTANT

MATHEMATICS>Chapter 8 - Quadrilaterals>EXERCISE>Q 17

A B C D

is a parallelogram.

P

is a point on

A D

such that

A P = 1 / 3 A D

.

Q

is a point on

B C

such that

C Q = 1 / 3 B C

. Prove that

A Q C P

is a parallelogram.

EASY

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IMPORTANT

MATHEMATICS>Chapter 8 - Quadrilaterals>EXERCISE>Q 18

In Figure,

P & Q

are mid points of the sides

A B

and

A C

respectively of

∆ A B C

. Also

D

and

E

are mid-points of

A P

and

A Q

respectivley. If

D E = 2.3 c m

and

B C = k cm

then find

k

.

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IMPORTANT

MATHEMATICS>Chapter 8 - Quadrilaterals>EXERCISE>Q 19

P, Q

and

R

are the mid points of

X O, Y O

and

Z O

respectively as shown in Figure. If

P Q = 4 c m, Q R = 6 c m

and

P R = 8 c m

, then find the lengths of the sides of

∆ X Y Z

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IMPORTANT

MATHEMATICS>Chapter 8 - Quadrilaterals>EXERCISE>Q 20

Prove that diagonals of a rectangle are equal in length.

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IMPORTANT

MATHEMATICS>Chapter 8 - Quadrilaterals>EXERCISE>Q 21

In Figure,

A B C D

is a rhombus whose side

A B

is produced to points

P

and

Q

such that

A P = A B = B Q . P D

and

Q C

are produced to meet at a point

R

. Show that

∠ P R Q = 90 °

.

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9th CBSE

IMPORTANT

MATHEMATICS>Chapter 8 - Quadrilaterals>EXERCISE>Q 22

If a diagonal of a parallelogram bisects one of the angles of the parallelogram, it also bisects the second angle and then the two diagonals are perpendicular to each other.

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IMPORTANT

MATHEMATICS>Chapter 8 - Quadrilaterals>EXERCISE>Q 23

A B C

is a triangle in which lines arc drawn through

A, B

and

C

parallel to the sides

B C, C A

and

A B

respectively forming

∆ P Q R

. Show that

B C = 1 / 2 Q R

.