Home
Class 10
MATHS
If a perpendicular is drawn from the ver...

If a perpendicular is drawn from the vertex containing the right angle of a right triangle to the hypotenuse then prove that the triangle on each side of the perpendicular are similar to each other and to the original triangle. Also, prove that the square of the perpendicular is equal to the product of the lengths of the two parts of the hypotenuse.

Promotional Banner

Topper's Solved these Questions

  • SURFACE AREAS AND VOLUMES

    RD SHARMA ENGLISH|Exercise All Questions|420 Videos

  • TRIGONOMETRIC IDENTITIES

    RD SHARMA ENGLISH|Exercise All Questions|254 Videos

Similar Questions

Explore conceptually related problems

Theorem 6.7 : If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

Show that in a right angled triangle, the hypotenuse is the longest side.

Find the area of a right triangle whose hypotenuse measures 17 cm and one of the other two sides 8 cm .

Draw a right triangle with hypotenuse of length 5\ c m and one side of length 4\ c mdot

Theorem 6.8 : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Prove that the area of right-angled triangle of given hypotenuse is maximum when the triangle is isosceles.

Prove that the area of right-angled triangle of given hypotenuse is maximum when the triangle is isosceles.

Find the area of the right-angled triangle with hypotenuse 40 cm and one of the other two sides 24 cm.

Draw a right triangle whose hypotenuse is of length 4\ c m and one side is of length 2. 5\ c mdot

In a right angled triangle, the hypotenuse is four times as long as the perpendicular drawn to it from the opposite vertex. One of the acute angle is

RD SHARMA ENGLISH-TRIANGLES-All Questions
  1. If A be the area of a right triangle and b one of the sides containing...

    Text Solution

    |

  2. In an equilateral triangle A B C if A D|B C , then A D^2 = (a)C D^...

    Text Solution

    |

  3. If a perpendicular is drawn from the vertex containing the right angle...

    Text Solution

    |

  4. Prove that the line segments joining the mid-points of the sides of a ...

    Text Solution

    |

  5. If a perpendicular is drawn from the vertex containing the right angle...

    Text Solution

    |

  6. In a right triangle A B C right-angled at B , if P a n d Q are points ...

    Text Solution

    |

  7. The diagonal B D of a parallelogram A B C D intersects the segment A E...

    Text Solution

    |

  8. ABC is a triangle in which AB = AC and D is a point on AC such that ...

    Text Solution

    |

  9. Two poles of height a metres and b metres are p metres apart. Prove th...

    Text Solution

    |

  10. In a triangle A B C , let P and Q be points on AB and AC respectively...

    Text Solution

    |

  11. A B C is an isosceles triangle with A B=A C and D is a point on A C su...

    Text Solution

    |

  12. If A B C D is quadrilateral and E and F are the mid-points of AC and B...

    Text Solution

    |

  13. Through the mid-point M of the side C D of a parallelogram A B C D , t...

    Text Solution

    |

  14. In a A B C ,D and E are points on sides A B a n d A C respectively su...

    Text Solution

    |

  15. Let A B C be a triangle and D and E be two points on side A B such tha...

    Text Solution

    |

  16. The side B C of a triangle A B C is bisected at D ; O is any point in ...

    Text Solution

    |

  17. In Figure, A B C is a triangle in which A B=A Cdot Point D and E are p...

    Text Solution

    |

  18. The bisector of interior angleA of triangleABC meets BC and D and the ...

    Text Solution

    |

  19. In three line segments OA ,OB and OC , point L ,M ,N respectively are ...

    Text Solution

    |

  20. O is any point inside a triangle A B C . The bisector of /A O B ,/B O ...

    Text Solution

    |