Question

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

Answer 1

Answer:

Step-by-step explanation:

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.