Home
Class 9
MATHS
In Figure, line l is the bisector of ang...

In Figure, line `l` is the bisector of angle `A` and `B` is any point on `l` . `B P` and `B Q` are perpendiculars from `B` to the arms of `Adot` Show that : `A P B~=A Q B` `B P=B Q` or `B` is equidistant from the arms of `/_A` . Figure

Text Solution

Verified by Experts

Given- `/_1=/_2`
`In /_AQB and /_APB`
`/_1=/_2`(given)
`AB=AB`(common)
`/_BQA=/_BPA`(each 90)
`/_AQB cong /_APB`(AAS)
`BQ=BP`.
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    RD SHARMA|Exercise All Questions|306 Videos

  • CONSTRUCTION

    RD SHARMA|Exercise All Questions|29 Videos

Similar Questions

Explore conceptually related problems

In Figure, line l is the bisector of angle A a n d B is any point on ldotB P a n d B Q are perpendiculars from B to the arms of Adot Show that: A P B ~= A Q B BP=BQ or B is equidistant from the arms of /_A

line l is the bisector of an angle /_A\ a n d/_B is any point on l. BP and BQ are perpendiculars from B to the arms of /_A . Show that: (i) DeltaA P B~=DeltaA Q B (ii) BP = BQ or B is equidistant from the arms of /_A

Line l is the bisector of an angleA and B is any point on I. BP and BQ are perpendiculars from B to the arms of angleA (see figure). Show that: DeltaAPB~=DeltaAQB

In the given figure, line l is the bisector of an angle angleA and B is any point on l. If BP and BQ are perpendiculars from B to the arms of angleA , show that (i) DeltaAPB~=DeltaAQB (ii) BP = BQ, i.e., B is equidistant from the arms of angleA .

Line l is the bisector of an angleA and B is any point on I. BP and BQ are perpendiculars from B to the arms of angleA (see figure). Show that: BP=BQ or B is equidistant from the arms of angleA .

In the given figure, line I is the bisector of an angle A and B is any point on I. BP and BQ are perpendiculars from B to the arms of angleA . Show that B is equidistant from the arms of angleA .

AB is a line segment and line l is its perpendicular bisector.If a point P lies on l show that P is equidistant from A and B.

AB is a line segment and line 1 is its perpendicular bisector.If a point P lies on 1 show that P is equidistant from A and B .

p A N D q are any two points lying on the sides D C a n d A D respectively of a parallelogram A B C Ddot Show that a r( A P B)=a r ( B Q C)dot

In the given figure, AB is a line segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B. Show that the line PQ is the perpendicular bisector of AB.

RD SHARMA-CONGRUENT TRIANGLE -All Questions
  1. In Figure, it is given that A B=B C and A D=E C . Prove that A B E~=C ...

    Text Solution

    |

  2. In Figure, l m and M is the mid-point of the line segment A Bdot Prov...

    Text Solution

    |

  3. In Figure, line l is the bisector of angle A and B is any point on l ....

    Text Solution

    |

  4. In Figure, O is the mid point of A B and C D . Prove that A O C~= B ...

    Text Solution

    |

  5. Prove that measure of each angle of an equilateral triangle is 60^0d...

    Text Solution

    |

  6. In Figure, it is given that A E=A D and B D=C Edot Prove that A E B~=...

    Text Solution

    |

  7. In Figure, it is given that A B=C F ,E F=B D and /A F E=/C B Ddot Prov...

    Text Solution

    |

  8. Two triangles are congruent if two sides and the included angle of o...

    Text Solution

    |

  9. In DeltaABC ,/A=100^0 and A B=A Cdot Find /B and /C

    Text Solution

    |

  10. Angles opposite to two equal sides of a triangle are equal. GIVEN : ...

    Text Solution

    |

  11. In Figure, X and Y are two points on equal sides A B and A C of a A B ...

    Text Solution

    |

  12. Prove that the angle between internal bisector of one base angle an...

    Text Solution

    |

  13. In A B C and P Q R Figure, A B=P Q ,B C=Q R and C B and R Q are extend...

    Text Solution

    |

  14. In Figure, the side B C of A B C is produced to form ray B D as shown....

    Text Solution

    |

  15. In a triangle the greater angle has the longer side opposite to it.

    Text Solution

    |

  16. If the bisectors of the base angles of a triangle enclose an angle ...

    Text Solution

    |

  17. If two sides of a triangle are unequal, the longer side has greater ...

    Text Solution

    |

  18. The bisectors of base angles of a triangle cannot enclose a right an...

    Text Solution

    |

  19. ABCD is a square, X and Y are points on sides AD and BC res...

    Text Solution

    |

  20. In figure, if P Q|P S ,P Q S R ,/S Q R=28^0 and /Q R T=65^0, then fin...

    Text Solution

    |