IMO Olympiad Work Book 9>Chapter 8 - Quadrilaterals>MATHEMATICAL REASONING>Q 9

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If the diagonal of a quadrilateral bisect each other at right angles, then it is a

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Important Questions on Quadrilaterals

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9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 8 - Quadrilaterals>MATHEMATICAL REASONING>Q 10

The measure of all the angles of a parallelogram, if an angle adjacent to the smallest angle is

24 °

less than twice the smallest angle is

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9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 8 - Quadrilaterals>MATHEMATICAL REASONING>Q 11

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral

P Q R S

, taken in order is rectangle if,

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9th Foundation

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IMO Olympiad Work Book 9>Chapter 8 - Quadrilaterals>MATHEMATICAL REASONING>Q 12

A B C D

is a parallelogram. If

A B

is produced to

E

such that

E D

bisects

B C

at

O

, then which of the following is correct?

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9th Foundation

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IMO Olympiad Work Book 9>Chapter 8 - Quadrilaterals>MATHEMATICAL REASONING>Q 13

D

And

E

are the mid-points of the sides

A B

and

A C

, respectively of

△ A B C

.

D E

is produced to

F .

To Prove that

C F

is equal and parallel to

D A,

we need an additional information which is-

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9th Foundation

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IMO Olympiad Work Book 9>Chapter 8 - Quadrilaterals>MATHEMATICAL REASONING>Q 14

X, Y

Are the mid-points of opposite sides

A B

and

D C

of a parallelogram

A B C D

.

A Y

And

D X

are joined intersecting in

S;

C X

and

B Y

joined intersecting in

R

. Then

S X R Y

is a

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IMO Olympiad Work Book 9>Chapter 8 - Quadrilaterals>MATHEMATICAL REASONING>Q 15

In a given figures, if

A B C D

is a rectangle and

P, Q

are the mid-points of

A D, D C

respectively. Then, the ratio of lengths

P Q

and

A C

is equal to

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9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 8 - Quadrilaterals>MATHEMATICAL REASONING>Q 16

In the given figure, $A B C D$ is a parallelogram in which $P$ is the mid-point of $D C$ and $Q$ is a point on $A C$ such that $C Q = \frac{1}{4} A C$ and $P Q$ product meet $B C$ at $R$ , then,

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9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 8 - Quadrilaterals>MATHEMATICAL REASONING>Q 17

If

A P B

and

C Q D

are two parallel lines, then the bisectors of the angles

A P Q, B P Q, C Q P

and

P Q D

form a