If two isosceles triangles have a common base, then the line joining their vertices bisects the base at right angles.

Asked by Topperlearning User | 10th Aug, 2017, 12:44: PM

Expert Answer:



ABC and DBC are two isosceles triangles with the common base, BC.

In ABD and ACD

AB = AC;

BD = CD;

AD = AD

ABD  ACD             (SSS congruence rule)

 
BAE = CAE                    (c.p.c.t)

In ABE and ACE

AB = AC;

BAE = CAE ;
  
  
AE = AE
 
ABE  ACE                                        (SAS congruence rule)

BEA = CEA and BE = EC                   (c.p.c.t)

BEA + CEA = 180o                                 (linear pair)

2BEA = 180o

  BEA = 90o

BEA = 90o = CEA

 
Hence, AD bisects the base BC at right angles.

Answered by  | 10th Aug, 2017, 02:44: PM