Home
Class 9
MATHS
AD, BE and CF , the altitudes...

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

Text Solution

AI Generated Solution

To prove that triangle ABC is an equilateral triangle given that the altitudes AD, BE, and CF are equal, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Given Information**: We know that the altitudes AD, BE, and CF of triangle ABC are equal. Let’s denote this common length as 'h'. 2. **Consider Triangles ABE and ACF**: ...
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    RD SHARMA ENGLISH|Exercise All Questions|306 Videos

  • CONSTRUCTION

    RD SHARMA ENGLISH|Exercise All Questions|40 Videos

Similar Questions

Explore conceptually related problems

A D ,\ B E\ a n d\ C F , the altitudes of A B C are equal. Prove that A B C is an equilateral triangle.

A D ,\ B E\ a n d\ C F , the altitudes of A B C are equal. Prove that A B C is an equilateral triangle.

Prove that the medians of an equilateral triangle are equal.

Prove that the medians of an equilateral triangle are equal.

If in a Delta ABC, cosA+ cosB + cosC =3/2. Prove that DeltaABC is an equilateral triangle.

AD and BE are respectively altitudes of triangle ABC such that AE=BD. Prove that AD=BE.

AD is a median of triangle ABC. Prove that : AB+BC+AC gt 2AD

AD is a median of triangle ABC. Prove that : AB+AC gt 2AD

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

If tan^3A+tan^3B+tan^3C=3tanA* tanB*tanC , then prove that triangle ABC is an equilateral triangle.

RD SHARMA ENGLISH-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. AD, BE and CF , the altitudes of triangle ABC are eq...

    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...

    Text Solution

    |

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

    Text Solution

    |

  7. Side Side Side(SSS) Congruence : Two triangles are congruent if the th...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. In ΔABC a n d\ Δ P Q R ,\ A B=P Q ,\ B C=Q R\ a n d\ C B\ a n d\ R Q...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. If D is the mid-point of the hypotenuse A C of a right triangle A B...

    Text Solution

    |