Please wait...
1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days
8104911739
For Business Enquiry

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this toll free number

022-62211530

Mon to Sat - 11 AM to 8 PM

prove ASA cogruency?

Asked by 1st June 2008, 9:38 PM
Answered by Expert
Answer:
We are given two triangles ABC and DEF in which:
angle B = E, C = F 
and BC = EF
We need to prove that ABC is congruent toDEF
For proving the congruence of the two triangles we consider three cases
Case (i) :Let AB = DE
And we have,B = E (Given)
BC = EF (Given)
So, triangle ABC is congruent to DEF (By SAS rule)
Case (ii) :Let if possible AB > DE. So, we can take a point P on AB such that
PB = DE. Now consider triangles PBC and  DEF
We have,
PB = DE (By construction)
B = E (Given)
BC = EF (Given)
So, we get
PBC is congruent toDEF, by the SAS
Since the triangles are congruent, their corresponding parts will be equal.
So, angle∠ PCB = ∠ DFE
But, we are given that
Angle ACB = ∠ DFE
So, angle ACB = PCB
But, this is possible only if P coincides with A.
or, BA = ED
So, ABC is congruent to DEF (by SAS axiom)
Case (iii) :If AB < DE, we can choose a point M on DE such that ME = AB and
By similar arguments as given in Case (ii), we can conclude that AB = DE and so,
Triangle ABC is congruent toDEF.
 
Answered by Expert 1st June 2008, 10:30 PM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer /10

Your answer has been posted successfully!

Chat with us on WhatsApp