Home
Class 9
MATHS
In the given figure, AC=AE, AB=AD and an...

In the given figure, `AC=AE, AB=AD` and `angleBAD=angleEAC`. Prove that `BC=DE`.

Text Solution

Verified by Experts

Since `angle1=angle2` (given)
`:. angle1+angle3=angle2+angle3` (adding same angle on both sides)
`implies" "angle BAC=angleDAE`
Now, in `DeltaBAC` and `DeltaDAE`
`:' {(AB=AD,"(given)"),(angleBAC=angleDAE,"(just proved)"),(AC=AE,"(given)"):}`
`:. DeltaBAC cong DeltaDAE` (SAS)
`:. BC=DE` (c.p.c.t) Hence Proved.
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    NAGEEN PRAKASHAN|Exercise Problems From NCERT/exemplar|5 Videos

  • TRIANGLES

    NAGEEN PRAKASHAN|Exercise Exercise 7a|35 Videos

  • SURFACE AREA AND VOLUME

    NAGEEN PRAKASHAN|Exercise Revision Exercise (long Answer Questions)|10 Videos

Similar Questions

Explore conceptually related problems

In the given figure, AB"||"DC and angleD=angleC . Prove that : (i) AD = BC (ii) AC = BD

In Figure,AC=AE,AB=AD and /_BAD=/_EAC Prove that BC=DE

In the adjoining figure, AB=EF, BC=DE, angleABC=angleFED=90^(@) , prove that AD = CF .

In the given figure, AB = AC and AD = AE. Prove that: DeltaABD~=DeltaACE

In the given figure,AB||EC,AB=AC and AE bisects /_DAC. Prove that:

In the given figure, AB=AD in DeltaABD and AC=AE in DeltaACE and angleBAD=angleEAC . Show that BC = DE .

In the given figure,AE =DE and BC|AD . Prove that the points A,B,C and D are concyclic.Also,prove that the diagonals of the quadrilateral ABCD are equal.

In figure, AB||DE, AB=DE, AC||DF and AC=DF. Prove that BC||EF and BC=EF.

In the given figure if DE||BC then find length AD

In the given figure, DB bot BC, DE bot AB and AC bot BC . Prove that (BE)/(DE)=(AC)/(BC)