Home
Class 9
MATHS
P Q R S is a square. P R and S Q interse...

`P Q R S` is a square. `P R` and `S Q` intersect at `Odot` State the measure of `/_P O Qdot`

Text Solution

Verified by Experts

`/_SPQ=90^@`
`/_QPO=1/2/_QPS=45^@`
`/_PQD=45^@`
`In /_QPO`
`/_OPQ+/_PQO+/_QOP+/_PQO=180^@`
`45+45+/_QOP=180`
`/_QOP=90^@`.
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA ENGLISH|Exercise All Questions|67 Videos

  • RATIONALISATION

    RD SHARMA ENGLISH|Exercise All Questions|130 Videos

Similar Questions

Explore conceptually related problems

P Q R S is a square such that P R\ a n d\ S Q intersect at Odot State the measure of /_P O Q

P Q R S is a square such that P R\ a n d\ S Q intersect at O . State the measure of /_P O Q .

P Q R S is a quadrilateral. P R\ a n d\ Q S intersect each other O . In which of the following cases, P Q R S is a parallelogram? (i) _∠P = 100°, ∠Q = 80°, ∠R = 95° (ii) /_P=85^0,\ /_Q=85^0,\ /_R=95^0 (iii) P Q=7C M ,\ Q R=7C M ,\ R S=8C M ,\ S P=8C M (iv) O P=6. 5 c m ,\ O Q=6. 5 c m ,\ O R=5. 2 c m ,\ O S=5. 2 c m

If P Q R S is a square, then write the measure of /_S R P

If P Q R S is a square, then write the measure of /_S R P

P Q and R S are two parallel chords of a circle and lines R P and S Q intersect each other at O as shown in Figure. Prove that O P=O Qdot

In Figure, P Q R S is a quadrilateral in which diagonals P R and Q S intersect in O . Show that P Q+Q R+R S+S P > P R+Q S PQ+QR+RS+SP<2 (PR+QS) Figure

In Figure, P Q R S is a parallelogram, P O and Q O are, respectively, the angle bisectors of /_P and /_Qdot Line L O M is drawn parallel to P Qdot Prove that : P L=Q M (ii) L O=O M

The adjacent figure P Q R S is a trapezium in which S P || R Q , find the measures of /_P\ a n d\ /_Rdot

P Q R S is a parallelogram. P X and QY are respectively, the perpendiculars from P and Q to S R and R S produced. Prove that P X=Q Ydot

RD SHARMA ENGLISH-QUADRILATERALS-All Questions
  1. Show that the diagonals of a square are equal and bisect each other...

    Text Solution

    |

  2. The diagonals of a rectangle A B C D meet at Odot If /B O C=44^0, find...

    Text Solution

    |

  3. P Q R S is a square. P R and S Q intersect at Odot State the measure o...

    Text Solution

    |

  4. ABCD is a rectangle in which diagonal AC bisects /A as well as /C ....

    Text Solution

    |

  5. A B C D is a rhombus with /A B C=56^0dot Determine /A C Ddot

    Text Solution

    |

  6. Each of the four angles of a rectangle is a right angle.

    Text Solution

    |

  7. Each of the four sides of a rhombus is of the same length.

    Text Solution

    |

  8. A B ,C D are two parallel lines and a transversal l intersects A B at ...

    Text Solution

    |

  9. If A B C and D E F are two triangles such that A B ,B C are respe...

    Text Solution

    |

  10. In Figure, A B C D is a parallelogram and X\ a n d\ Y are points on th...

    Text Solution

    |

  11. In Figure, A B C is an isosceles triangle in which A B=A Cdot and C P|...

    Text Solution

    |

  12. In Figure, X ,Y are the mid-points of opposite sides A B and D C of a ...

    Text Solution

    |

  13. Two segments A C and B D bisect each other at O . Prove that A B C D i...

    Text Solution

    |

  14. Each of the angles of a square is a right angle and each of the four ...

    Text Solution

    |

  15. The diagonals of a rectangle are of equal length.

    Text Solution

    |

  16. If the diagonals of a quadrilateral bisect each other, then the qua...

    Text Solution

    |

  17. A quadrilateral is parallelogram if its opposite angles are equal.

    Text Solution

    |

  18. A quadrilateral is a parallelogram if its opposite sides are equal.

    Text Solution

    |

  19. In Figure, A B C D is a parallelogram in which /A=60^0 . If the bisect...

    Text Solution

    |

  20. Show that if the diagonals of a quadrilateral are equal and bisect eac...

    Text Solution

    |