Home
Class 9
MATHS
A B C is a triangle. D is a point on A B...

`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`

Text Solution

Verified by Experts

A is a common angle in `/_\ABC `and `/_\ADE`
here `(AD)/(AB)=(AE)/(AC)=1/4`
therefore ,`/_\ABC ~ /_\ ADE` ( SAS)
`(DE)/(BC)=(AD)/(AB)=(AE)/(AC)=1/4`
so `DE=(1/4)BC`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA|Exercise All Questions|67 Videos

  • RATIONALISATION

    RD SHARMA|Exercise All Questions|130 Videos

Similar Questions

Explore conceptually related problems

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

A B C D is a parallelogram. P is a point on A D such that A P=1/3\ A D\ a n d\ Q is a point on B C such that: C Q=1/3B Cdot Prove that A Q C P is a parallelogram.

A B C D is a parallelogram. E is a point on B A such that B E=2\ E A\ a n d\ F is a point on D C such that D F=2\ F Cdot Prove that A E\ C F is a parallelogram whose area is one third of the area of parallelogram A B\ C Ddot

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F Cdot Prove that: a r\ \ E G B)=1/6a r\ (A B C D)

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F Cdot Prove that: a r\ (\ E B G)=a r\ (\ E F C)

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F Cdot Prove that: a r\ (\ E F C)=1/2\ a r\ (\ E B F)

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F Cdot Prove that: a r\ (A D E G)=\ a r\ (G B C E)

A B C D is a parallelogram, G is the point on A B such that A G=2G B ,E is a point of D C such that C E=2D E and F is the point of B C such that B F=2F Cdot Prove that : a r(A D E G)=a r(G B C E) a r( E G B)=1/6a r(A B C D)

In Figure, A B C D is a parallelogram in which P is the mid-point of D C\ a n d\ Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C\ a t\ R , prove that R is a mid-point of B C

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

RD SHARMA-QUADRILATERALS-All Questions
  1. In figure A B=A C\ a n d\ C P||B A and A P is the bisector of exter...

    Text Solution

    |

  2. Let A B C be an isosceles triangle in which AB=AC If D , E , F be th...

    Text Solution

    |

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

    Text Solution

    |

  4. In Figure, A B C D is a parallelogram in which P is the mid-point o...

    Text Solution

    |

  5. In Figure, A B C D\ a n d\ P Q R C are rectangles and Q is the mid-poi...

    Text Solution

    |

  6. A B C D is a parallelogram, E\ a n d\ F are the mid-points of A B\ a n...

    Text Solution

    |

  7. B M\ a n d\ C N are perpendicular to a line passing through the vert...

    Text Solution

    |

  8. Show that the line segments joining the mid-points of the opposite s...

    Text Solution

    |

  9. Fill in the blanks to make the following statements correct The tr...

    Text Solution

    |

  10. In a parallelogram A B C D , write the sum of angle A\ a n d\ B

    Text Solution

    |

  11. In a parallelogram A B C D , if /D=115^@, then write the measure of ...

    Text Solution

    |

  12. P Q R S is a square such that P R\ a n d\ S Q intersect at Odot State ...

    Text Solution

    |

  13. In a quadrilateral A B C D , bisectors of angles A\ a n d\ B intersect...

    Text Solution

    |

  14. The diagonals of a rectangle A B C D\ meet at O . If /B O C=44^@, f...

    Text Solution

    |

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

    Text Solution

    |

  16. If A B C D is a rectangle with /B A C=32^@, find the measure of /D B C

    Text Solution

    |

  17. If A B C D is a rhombus with /A B C=56^@, find the measure of /A C D

    Text Solution

    |

  18. The perimeter of a parallelogram is 22cm. If the longer side measur...

    Text Solution

    |

  19. If the angles of a quadrilateral are in the ratio 3:5:9:13, then find ...

    Text Solution

    |

  20. If the bisectors of two adjacent angles A\ a n d\ B of a quadrilate...

    Text Solution

    |