Question

If altitudes BD and CEof triangle ABC are equal, then AB = ? .​

Answer 1

Answer:

AC

Step-by-step explanation:

In triangle BDC and triangle CEB

Angle BEC= Angle CDB= 90 (given)

BD=CE (given)

BC=BC (common)

By R.H.S Congruency

triangle BDC ≡ triangle CEB

By CPCT

angle EBC = angle DCB

angle ABD+DBC= Angle ACE+ECB

[ angle DBC = angle ECB ] ( Given BD=CE angles opp. to equal sides are equal)

(Angle ABD= Angle ACE ) = ( Angle DBE=Angle ECD)

In triangle ABD and triangle ACE

Angle A = Angle A

BD=CE (given)

angle DBE= angle ECD (proved)

By AAS congruency

Triangle ABD ≡ Triangle ACE

By CPCT

AB=AC

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