Home
Class 10
MATHS
ABC is an isosceles triangle with AC=BC....

ABC is an isosceles triangle with AC=BC.If `AB^2=2AC^2`.prove that ABC is a right triangle.

Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    R G PUBLICATION|Exercise EXERCISE|108 Videos

  • SURFACE AREA AND VOLUMES

    R G PUBLICATION|Exercise EXERCISE|69 Videos

Similar Questions

Explore conceptually related problems

In an isosceles triangle ABC if AC=BC and AB^2 = 2AC^2 , prove that /_C is a right angle.

ABC is an isosceles triangle right angled at C.Prove that AB^2=2AC^2 .

In an isosceles triangleABC if AC=BC and AB^2=2AC^2 then what is the measure of angleC ?

In FIg. 6.40, E is a point on side CB produced of an isosceles triangle ABC with AB=AC. If AD_|_BC and EF_|_AC , prove that triangleABD~triangleECF .

∆ABC is an isosceles triangle in which /_C = 90° . If AC = 6 cm , Then AB is

ABC is an isosceles triangle with AB = AC and D is a point on AC such that BC^2=ACxxCD . Prove that BD = BC

In the triangle ABC, BC = m^2 -n^2 , AC =3 mn and AB = m^2+n^2 . Prove that it is a right angled triangle.

In the triangle ABC,AB=p^2-q^2,BC=p^2+q^2 and CA=2pq then prove that triangleABC is right angled.Which of the angles of the triangle is right angle?

In ∆ABC , AD _|_ BC such that AD^2 = BD.CD . Prove that ∆ABC is right angled at A.

In an isosceles triangle ABC if AB = AC= 15 cm and BC =18 cm, find the values of cos /_ABC and sin /_ABC .

R G PUBLICATION-TRIANGLES-EXERCISE
  1. In Fig.6.53,ABD is a triangle right angle at A and AC|BD.Show that (i...

    Text Solution

    |

  2. ABC is an isosceles triangle right angled at C.Prove thatAB^2=2AC^2.

    Text Solution

    |

  3. ABC is an isosceles triangle with AC=BC.If AB^2=2AC^2.prove that ABC i...

    Text Solution

    |

  4. ABC is an equilateral triangle of sides 2a.Find each of its altitudes.

    Text Solution

    |

  5. Prove that the sum of the squares of the sides of a rhombus is equal t...

    Text Solution

    |

  6. In Fig.6.45,O is a point in the interior of a triangle ABC,OD|BC,OE|AC...

    Text Solution

    |

  7. Fig.6.45,O is a point in the interior of a triangle ABC,OD|BC,OE|AC an...

    Text Solution

    |

  8. A ladder 10 m long reaches a window 8m above the ground. Find the dist...

    Text Solution

    |

  9. A guy wire attached to a vertical pole of heigh 18 m is 24 m long and ...

    Text Solution

    |

  10. An aeroplane leaves an airport and flies due north at a speed of 1000 ...

    Text Solution

    |

  11. Two poles of heights 6 m and 11 m stand on a plane ground. If the dist...

    Text Solution

    |

  12. D and E are points on the sides CA and CB respectively of a triangle A...

    Text Solution

    |

  13. The perpendicular from A on side BC of atriangleABC intersects BC at ...

    Text Solution

    |

  14. In an equilateral triangle ABC, D is a point on side BC such that BD =...

    Text Solution

    |

  15. In an equilateral triangle, prove that three times the square of one s...

    Text Solution

    |

  16. Tick the correct answer and a justify :In triangleABC,AB=6sqrt3,AC=12c...

    Text Solution

    |

  17. In Fig.6.56,PS is the bisector of angleQPR of trianglePQR.Prove that (...

    Text Solution

    |

  18. In Fig.6.57, D is point on hypothenuse AC of triangleABC,such thatBD|A...

    Text Solution

    |

  19. In Fig.6.58, ABC is a triangle in which angleABC>90^@ and AD|CBproduce...

    Text Solution

    |

  20. In Fig.6.59, ABC is a triangle in which angleABC<90^@ and AD|BC.Prove ...

    Text Solution

    |