Home
Class 10
MATHS
Let A B C be a triangle and Da n dE be t...

Let `A B C` be a triangle and `Da n dE` be two points on side `A B` such that `A D=B Edot` If `D P B C` and `E Q A C ,` THEN PROVE THAT `P Q A Bdot`

Text Solution

Verified by Experts

In triangle ABC we have,
`DP||BC` and `EQ||AC`
Then, `(AD)/(DB)=(AP)/(PC)`
`(BE)/(EA)=(BQ)/(QC)`
...
Promotional Banner

Topper's Solved these Questions

  • SURFACE AREAS AND VOLUMES

    RD SHARMA|Exercise All Questions|417 Videos

  • TRIGONOMETRIC IDENTITIES

    RD SHARMA|Exercise All Questions|254 Videos

Similar Questions

Explore conceptually related problems

A B C D is a trapezium in which A B D C . P and Q are points on sides A D and B C such that P Q A B . If P D=18 , B Q=35 and Q C=15 , find A D .

A B C is a triangle, P is a point on A Ba n dQ is a point on A C such that /_A Q P=/_A B Cdot Complete the relation (A r e aof A P Q)/(A r e aof A B C)=dot(())/(A C^2) .

In Figure, B D and C E are two altitudes of a A B C such that B D=C Edot Prove that A B C is isosceles. Figure

In Figure, A B C is a triangle in which /_B=2/_C . D is a point on side B C such that A D bisects /_B A C a n d A B=C DdotB E is the bisector of /_B . The measure of /_B A C is 72^0 (b) 73^0 (c) 74^0 (d) 96^0

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

A B C is a triangle. D is a point on A B such that D=1/4A B\ a n d\ E is a point on A C such that A E=1/4A Cdot Prove that D E=1/4B C

In A B C , P and Q are points on sides A B and A C respectively such that P Q B C . If A P=4c m ,\ \ P B=6c m and P Q=3c m , determine B C .

In a A B C , P and Q are point on the sides A B and A C respectively, such that P Q B C . If A P=2. 4 c m , A Q=2c m , Q C=3c m and B C=6c m , find A B and P Q .

In 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=1/4A Cdot If P Q produced meets B C at Rdot Prove that R is a mid-point of B Cdot

Let A B C be an isosceles triangle with A B=A C and let D ,\ E ,\ F be the mid points of B C ,\ C A\ a n d\ A B respectively. Show that A D_|_F E\ a n d\ A D is bisected by F E

RD SHARMA-TRIANGLES-All Questions
  1. Through the mid-point M of the side C D of a parallelogram A B C D , t...

    Text Solution

    |

  2. In a A B C ,D and E are points on sides A Ba n dA C respectively such...

    Text Solution

    |

  3. Let A B C be a triangle and Da n dE be two points on side A B such tha...

    Text Solution

    |

  4. The side B C of a triangle A B C is bisected at D ;o is any point in A...

    Text Solution

    |

  5. In Figure, A B C is a triangle in which A B=A Cdot Point Da n dE are p...

    Text Solution

    |

  6. In the given figure The bisector of interior /A of A B C meets B C in...

    Text Solution

    |

  7. In three line segments O A ,O Ba n dO C , point L ,M ,N respectively a...

    Text Solution

    |

  8. O is any point inside a triangle A B C . The bisector of /A O B ,/B O ...

    Text Solution

    |

  9. ABCD is a quadrilateral in which AB=AD . The bisector of  BAC A...

    Text Solution

    |

  10. In A B C ,D is the mid-point of B Ca n dE D is the bisector of the /A...

    Text Solution

    |

  11. A D is a median of Delta A B C . The bisector of /A D B and /A D C...

    Text Solution

    |

  12. In Figure, A B C is a right triangle right angled at B and points Da n...

    Text Solution

    |

  13. In a triangle A B C , the angles at Ba n dC are acute. If B Ea n d C ...

    Text Solution

    |

  14. Prove that in any triangle the sum of squares of any to sides is equal...

    Text Solution

    |

  15. AD is an altitude of an equilateral triangle ABC. On AD as base...

    Text Solution

    |

  16. A ladder 15 m long reaches a window which is 9m above the ground on on...

    Text Solution

    |

  17. Prove that three times the sum of the squares of the sides of a tri...

    Text Solution

    |

  18. In Figure, D , E are points on sides A B and A C respectively of A...

    Text Solution

    |

  19. In the trapezium ABCD,AC and BD intersect at O and also AB=2CD If the ...

    Text Solution

    |

  20. ABC is an isosceles triangle right-angled at B. Similar triangles ...

    Text Solution

    |