Home
Class 9
MATHS
In isosceles triangle ABC, sides AB and ...

In isosceles triangle ABC, sides AB and AC are equal. If point D lies in base BC and point E lies on BC produced (BC being produced through vertex C), prove that :
(i) `AC gt AD`
(ii) `AE gt AC`
(iii) `AE gt AD`

Text Solution

Verified by Experts

The correct Answer is:
(i) `z lt y lt x" (ii) "AB gt BC gt AC`
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES

    ICSE|Exercise EXERCISE 11|42 Videos

  • INDICES [EXPONENTS]

    ICSE|Exercise EXERCISE 7 (C)|19 Videos

  • ISOSCELES TRIANGLES

    ICSE|Exercise EXERCISE 10 (B)|4 Videos

Similar Questions

Explore conceptually related problems

From the following figure, prove that : (i) AB gt BD (ii) AC gt CD (iii) AB+AC gt BC

Find : (i) BC (ii) AD (iii) AC

In isosceles triangle ABC, D is a point on the base BC produced. Prove that AD gt AB .

In the figure, given alongside, AD bisects angle BAC. Prove that : (i) AB gt BD (ii) AC gt CD (iii) AB+AC gt BC

In the figure, given alongside, AD bisects angle BAC. Prove that : (i) AB gt BD (ii) AC gt CD (iii) AB+AC gt BC

In a quadrilateral ABCD, prove that : (i) AB+BC+CD gt DA (ii) AB+BC+CD+DA gt 2AC (iii) AB+BC+CD+DA gt 2BD

ABC is an isosceles triangle with AB = AC = 2a and BC = a . If AD bot BC, find the length of AD .

In triangle ABC, AB gt AC and D is a point in side BC. Show that : AB gt AD .

In triangle ABC, AB gt AC and D is a point in side BC. Show that : AB gt AD .

In an isosceles triangle ABC, AB = AC and D is a point on BC produced. Prove that : AD^(2)=AC^(2)+BD.CD

ICSE-INEQUALITIES-EXERCISE 11
  1. In a triangle PQR, QR = PR and angleP=36^(@). Which is the largest sid...

    Text Solution

    |

  2. If two sides of a triangle are 8 cm and 13 cm, then the length of the ...

    Text Solution

    |

  3. In each of following figures, write BC, AC and CD in ascending order o...

    Text Solution

    |

  4. Arrange the sides of DeltaBOC in descending order of their lengths. BO...

    Text Solution

    |

  5. D is a point in side BC of triangle ABC. If AD gt AC, show that AB gt ...

    Text Solution

    |

  6. In the following figure, angleBAC=60^(@)" and "angleABC=65^(@). Prov...

    Text Solution

    |

  7. In the following figure , AC = CD, angleBAD=110^(@)" and " angleACB=...

    Text Solution

    |

  8. From the following figure, prove that : (i) AB gt BD (ii) AC gt CD...

    Text Solution

    |

  9. In a quadrilateral ABCD, prove that : (i) AB+BC+CD gt DA (ii) AB+B...

    Text Solution

    |

  10. In the following figure, ABC is an equilateral triangle and P is any p...

    Text Solution

    |

  11. P is any point inside the triangle ABC. Prove that : angleBPC gt angle...

    Text Solution

    |

  12. Prove that the straight line joining the vertex of an isosceles triang...

    Text Solution

    |

  13. In the following diagram, AD = AB and AE bisects angle A. Prove that :...

    Text Solution

    |

  14. The sides AB and AC of a triangle ABC are produced, and the bisectors ...

    Text Solution

    |

  15. In the following figure, AB is the largest side and BC is the smallest...

    Text Solution

    |

  16. In quadrilateral ABCD, side AB is the longest and side DC is the short...

    Text Solution

    |

  17. In triangle ABC, side AC is greater than side AB. If the internal bise...

    Text Solution

    |

  18. In isosceles triangle ABC, sides AB and AC are equal. If point D lies ...

    Text Solution

    |

  19. Given : ED = EC Prove : AB+AD gt BC.

    Text Solution

    |

  20. In triangle ABC, AB gt AC and D is a point in side BC. Show that : AB ...

    Text Solution

    |