Home
Class 9
MATHS
In given figure the altitudes AD, BE and...

In given figure the altitudes AD, BE and CF , the altitudes of triangle ABC are equal. Prove that ABC is an equilateral triangle.

Text Solution

Verified by Experts

`In /_ADC and /_BEC`
`/_D=/_E`(each 90)
AD=BE(given)
`/_C=/_C`(common)
`/_ADC cong /_BEC)(A A S)`
`AC=BC`-(1)
`In /_ADB and /_CFB`
`/_D=/_F`(each 90)
...
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

AD,BE and CF, the altitudes of ABC are equal.Prove that ABC is an equilateral triangle.

AD,BE and CF, the altitudes of ABC are equal.Prove that ABC is an equilateral triangle.

Angle A,B,C of a triangle ABC are equal to each other.Prove that ABC is equilateral.

Find the perimeter of the given figure : BCDE is a square and ABC is an equilateral triangle.

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see figure). Show that AB=AC, i.e., ABC is an isosceles triangle.

In the given figure, BD and CE are the altitudes of triangle ABC such that BD = CE, then angleDCB=

In the given figure, BD and CE are the altitudes of triangle ABC such that BD = CE, then DeltaCBD is congruent to

If AD,BE,CF are the altitudes of triangle ABC whose ortho centre is H then C is ortho centre of

If AD, BE and CF are medians of triangle ABC then prove that median AD divides line segment EF.

BE and CF are two equal altitudes of a triangle ABC.Using RHS congruence rule,prove that the triangle ABC is isosceles

RD SHARMA-CONGRUENT TRIANGLE -All Questions
  1. If the bisector of the exterior vertical angle of a triangle be par...

    Text Solution

    |

  2. Prove that Two right triangles are congruent if the hypotenuse and o...

    Text Solution

    |

  3. In given figure the altitudes AD, BE and CF , the altitudes of triang...

    Text Solution

    |

  4. A point O is taken inside an equilateral four sided figure A B C D suc...

    Text Solution

    |

  5. In Delta P Q R , if P Q=Q R and L ,M and N are the mid-points ...

    Text Solution

    |

  6. If two isosceles triangles have a common base, prove that the line ...

    Text Solution

    |

  7. A B C and D B C are two isosceles triangles on the same base B C ...

    Text Solution

    |

  8. Explain -Side Side Side(SSS) Congruence .

    Text Solution

    |

  9. A B C D is a parallelogram, if the two diagonals are equal, find th...

    Text Solution

    |

  10. In a A B C , it is given that A B=A C and the bisectors of /B a...

    Text Solution

    |

  11. A B C is a triangle in which /B =2 /CdotD is a point on B C s...

    Text Solution

    |

  12. In A B C ,\ /A=100^0a n d\ A B=A Cdot Find /B\ a n d\ /C

    Text Solution

    |

  13. In Figure, A B=A C\ a n d\ /A C D=120^0dot Find /A

    Text Solution

    |

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

    Text Solution

    |

  15. In Figure O is the mid-point of A B\ a n d\ C Ddot Prove that \ A O C...

    Text Solution

    |

  16. In Figure, it is given that A B=C F ,\ E F=B D\ a n d\ /A F E=\ /C B...

    Text Solution

    |

  17. In Figure, it is given that A E=A D\ a n d\ B D=C Edot Prove that A...

    Text Solution

    |

  18. Given: In /\ABC and /\PQR, A B=P Q ,\ B C=Q R\ a n d\ C B\ a n d\ R ...

    Text Solution

    |

  19. In Figure, X ,\ Y\ are two points on equal sides A B\ a n d\ A C of...

    Text Solution

    |

  20. Suppose line segments A B\ a n d\ C D intersect at O in such a way tha...

    Text Solution

    |