Home
Class 10
MATHS
In Figure, D , E are points on sides A ...

In Figure, `D , E` are points on sides `A B` and `A C` respectively of ` A B C ,` such that `a r( B C E)=a r( B C D)dot` Show that `D E B Cdot`

Text Solution

Verified by Experts

Given D and E are point on sides AB and AC respectively of triangle ABC such that Area(ΔDBC) = Area(ΔEBC).
Given that `Area(ΔDBC) = Area(ΔEBC).`
Then the height of triangle DBC and Triangle EBC are the same because both triangles are the same
...
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

D and E are points on sides AB and AC respectively of DeltaA B C such thata r" "(D B C)" "=" "a r" "(E B C) . Prove that D E" "||" "B C .

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r( A D F)=a r( D C E)dot

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

A point D is taken on the side B C of a A B C such that B D=2d Cdot Prove that a r( A B D)=2a r( A D C)dot

Triangles A B C and +DBC are on the same base B C with A, D on opposite side of line B C , such that a r(_|_ A B C)=a r( D B C)dot Show that B C bisects A Ddot

In a A B C , D and E are points on the sides A B and A C respectively such that D E B C If A D=6\ c m , D B=9\ c m and A E=8\ c m , find A C . (ii) If (A D)/(D B)=3/4 and A C=15\ c m , find A E . (iii) If (A D)/(D B)=2/3 and A C=18\ c m , find A E .

In a A B C , D a n d E are points on the sides A B and A C respectively. For each of the following cases show that D E B C : A B=12 c m , A D=8 c m , A E=12 c m a n d A C=18 c m . (ii) A B=5. 6 c m , A D=1. 4 c m , A C=7. 2 c m a n d A E=1. 8 cm

In Figure D\ a n d\ E are two points on B C such that B D=D E=E Cdot Show that a r(\ A B D)=\ a r\ (\ A D E)=a r\ (\ A E C)dot

In a A B C , D and E are points on the sides A B and A C respectively such that D E B C If A D=4 , A E=8 , D B=x-4 , and E C=3x-19 , find x (ii) If A D=8 c m , A B=12 c m and A E=12 c m , find C E . (iii) If A D=4 c m , D B=4. 5 c m and A E=8 c m , find A C .

In a A B C , D and E are points on the sides A B and A C respectively such that D E B C If A D=2 c m , A B=6 c m and A C=9 c m , find A E . (ii) If (A D)/(B D)=4/5 and E C=2. 5 c m , find A E . (iii) If A D=x , D B=x-2 , A E=x+2 and E C=x-1 , find the value of x .

RD SHARMA-TRIANGLES-All Questions
  1. A ladder 15 m long reaches a window which is 9m above the ground on on...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. ABC is a right triangle right-angled at B. Let D and E be any points o...

    Text Solution

    |

  7. A girl of height 90 cm is walking away from the base of a lamp-post...

    Text Solution

    |

  8. If A B C is a right triangle right-angled at Ba n dM ,N are the mid-...

    Text Solution

    |

  9. Determine whether the triangle having sides (a-1)c m ,2sqrt(a)c m and ...

    Text Solution

    |

  10. If triangle A B C is similar to triangle D E F such that B C=3C M ...

    Text Solution

    |

  11. The perimeters of two similar triangles are 30cm and 20cm respectively...

    Text Solution

    |

  12. Two triangles B A Ca n dB D C , right angled at Aa n dD respectively, ...

    Text Solution

    |

  13. ABC is a right angle triangle right angled at A. A circle is inscribed...

    Text Solution

    |

  14. In Figure, /B A C=90^0,A D is its bisector. If D E|A c , prove that D...

    Text Solution

    |

  15. Prove that the line segments joints joining the mid-points of the a...

    Text Solution

    |

  16. In figure, P is the mid-point of B C , ,Q is the mid-point of A P ,...

    Text Solution

    |

  17. A vertical stick 12m long casts a shadow 8m long on the ground. At the...

    Text Solution

    |

  18. In a quadrilateral A B C D , if bisectors of the /A B Ca n d/A D C mee...

    Text Solution

    |

  19. In A B C , the bisector of /B meets A C at Ddot A line P Q A C meets...

    Text Solution

    |

  20. The bisectors of the angles B and C of a triangle A B C , meet the o...

    Text Solution

    |