Home
Class 9
MATHS
The side BC of DeltaABC is produced ot D...

The side BC of `DeltaABC` is produced ot D. The bisector of `angleA` meets BC at E. Prove that `angleABC+angleACD=2angleAEC`.

Text Solution

Verified by Experts

Side BE of `DeltaABE` has been produced to C.
`:.angleAEC=angleABE+angleBAE`
`impliesangleAEC=angleABC+(1)/(2)angleA`
`implies2angleAEC=2angleABC+angleA" "....(i)`
Again, side BC of `DeltaABC` has been produced to D.
`:.angleACD=angleACD+angleA." "....(ii)`
On subtracting (ii) from (i), we get
`2angleAEC-angleACD=angleABC`
`:.angleABC+angleACD=angleACD=2angleAEC`.
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    RS AGGARWAL|Exercise Exercise 8|13 Videos
  • TRIANGLES

    RS AGGARWAL|Exercise EXERCISE|16 Videos
  • TRIANGLES

    RS AGGARWAL|Exercise MULTIPLE-CHOICE QUESTIONS (MCQ)|10 Videos
  • QUADRILATERALS

    RS AGGARWAL|Exercise Matching of Columns:|2 Videos
  • VOLUME AND SURFACE AREA OF SOLIDS

    RS AGGARWAL|Exercise Multiple Choice Questions (Mcq)|73 Videos

Similar Questions

Explore conceptually related problems

The side BC of DeltaABC is product to N. bisector of angle meets BC at M. Prove that angleABC+angleACN=2angleAMC

The side BC of a triangle ABC is produced to D, bisector of the angle ABC and ACD meet at P. If angleBPC =x^(@) and angleBAC = y^(@) , then which one of the following is correct ?

The side BC of Delta ABC is produced to D. If angleACD = 108^(@) and angleB = 1/2 angleA then angleA is

The side BC of a ABC is produced,such that D is one ray BC. The bisector of /_A meets BC in L as shown in Figure.Prove that /_ABC+/_ACD=2/_ALC

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

The sides BC of ABC is product to a point D The bisector of /_A meets side BC in L. If /_ABC=30^(@) and /_ACD=115^(@), find /_ALC

Let ABC be a triangle such that AB = 15 and AC = 9. The bisector of angleBAC meets BC in D. If angleACB = 2angleABC , then BD is

The side BC of DeltaABC is produced to D. If angleACD=114^(@) and angleABC=((1)/(2)) angleBAC , what is the value (in degrees) of angleBAC ?

The side BC of a DeltaABC is extended to D. If angleACD = 120^(@) and angleABC =(1)/(2)angleCAB , then the value of angleABC is