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In Fig BD and CE are altitudes of bigtriangleup ABC such that BD= CE. State the three pairs of equal parts in bigtriangleup CBD and bigtriangleup BCE. Is bigtriangleup CBD cong bigtriangleup BCE ? Why or why not?

3. In Fig 7.33, BD and CE are altitudes of \bigtriangleup ABC such that BD= CE.

          (i) State the three pairs of equal parts in \bigtriangleup CBD and \bigtriangleup BCE.
          (ii) Is \bigtriangleup CBD\cong \bigtriangleup BCE ? Why or why not?
          (iii) Is \angle DCB= \angle EBC ? Why or why not?

                    

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i) Given,  in \bigtriangleup CBD and \bigtriangleup BCE.

BD= CE

\angle CEB=\angle BDC=90^o 

\overline{ BC} = \overline{ CB}

 

ii) So, By RHS Rule of congruency, we conclude:

\bigtriangleup CBD\cong \bigtriangleup BCE

 

iii) Since both the triangle are congruent, all parts of one triangle are equal to their corresponding part from another triangle.

So.

\bigtriangleup CBD\cong \bigtriangleup BCE.

 

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