Home
Class 9
MATHS
In following figure if AD if the bisecto...

In following figure if AD if the bisector of `angleABC,` then prove that `AB gt BD`

Text Solution

Verified by Experts

Given ABC is a triangle such that AD is the bisector of `angleABC`
To Prove `AB gt BD`
Proof Since ,AD if the bisector of `angleBAC.`
`therefore " "angleBAD =CAD " "….(i)`
`" But " " "angleADB gt angleCAD `
[exterior angle of a triangle is greater than each of the opposite interior angle ]
` therefore " "angleABD gt angle CAD " "["from Eq.(i)"]`
`rArr " " AB gt BD " "["side opposite to greater angle is longer "]`
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|21 Videos

  • TRIANGLES

    NCERT EXEMPLAR ENGLISH|Exercise VERY SHORT ANSWER TYPE QUESTIONS|12 Videos

  • STATISTICS AND PROBABILITY

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|12 Videos

  • VOLUME AND SURFACE AREA

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|8 Videos

Similar Questions

Explore conceptually related problems

In the following figure is CD the perpendicular bisector of AB ?

ABC is a right triangle with AB = AC .If bisector of angle A meet BC at D then prove that BC = 2 AD .

If D any point on the BC of an isosceles triangle ABC then prove that AB gt AD and AC gt AD .

In the following figure, if AD = DE . Prove that : AB+BC gt CE

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

In the following figure , AB = BC , AD bot BC and CE bot AB . prove that AD = CE

In the following diagram, AD = AB and AE bisects angle A. Prove that : (i) BE = DE (ii) angleABD gt angleC

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

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