Question

BD and CE are the altitude of triangle ABC such that BD=CE (i)state the three pairs of equal parts in triangle CBD and triangle BCE A (ii) is triangle CBD congruent to triangle ACE (iii) is angle DCB =angle EBC

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Answer 1

Answer:

By RHS congruence condition if hypotenuse and one side of one right triangle are equal to hypotenuse and one side of other right triangle then both right triangles are congruent.

It is given that BD=CE and BC is the hypotenuse of small triangles CEB and BDC

So, In right triangles BCD and CBE

BC=CB=common side⋯⋯[hypotenuse]

And BD=CE=given⋯⋯[sides of right triangles]

So, by RHS condition

△BCD≅△CBE

From above, we can see that three pairs of matching part are two equal sides which are used for RHS test and other id right angle of both triangles which need not to be written when using RHS.

I hope it's helpful..

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Answer 2

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(i) In CBD and BCE,

the three pairs of equal parts are as given below:

BEC = CDB (=90)

BD = CE (Given)

and BC= BC (Common in both)

(ii) From (i) above, CBD BCE (By RHS congruence rule)

(iii) Yes, DCB = EBC (Corresponding parts of congruent triangles)