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Standard X

Mathematics

Properties of Cyclic Quadrilateral

23. In the gi...

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23. In the given figure, P, Q and R are the mid-points of sides AB, AC and BC of AABC respectively If ADBC, then prove that PQRD is a cyclic quadrilateral. D R [(C)" ()" ()oz .(v)61 .suy]

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Question 4
P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such that $A C ⊥ B D$ . Prove that PQRS is a rectangle.

P, Q, R

and

S

are respectively the mid-points of the sides

A B, B C, C D

and

D A

of a quadrilateral

A B C D

such that

A C ⊥ B D

. Prove that

P Q R S

is a rectangle.

Q. Question 5
P, Q, R and S are respectively the mid-points of sides AB, BC, CD and DA of quadrilateral ABCD in which AC = BD and

A C ⊥ B D

. Prove that PQRS is a square.

□ A B C D

is a quadrilateral

P, Q, R, S

are the mid point of side

A B, B C, C D, A C

respectively. Prove that

□ P Q R S

is a parallelogram.

Q. In the quadrilateral given below,

A D = B C . P, Q, R

and

S

are mid-points of

A B, B D, C D

and

A C

respectively. Prove that

P Q R S

is a rhombus.

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