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CBSE Class 9 Answered

In figure, two isosceles triangles have a common base, prove that line segment joining their vertices bisects the common base at right angles.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

In ABD and ACD,

AB = AC (given)

BD = DC (given)

AD = AD (common)

Therefore, ABD ACD (By SSS rule)

So, BAD = CAD (By cpct) ... (1)

In ABE and ACE,

AB = AC (given)

AE = AE (common)

BAD = DAC (By (1)) ...(2)

Therefore, ABE ACE (By SAS)

BE = CE (By cppt)

And, BEA = CEA (cpcpt)

But, BEA + CEA = 180o

BEA = 90o

Answered by | 04 Jun, 2014, 03:23: PM

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