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Congruence of Triangles

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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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P Pankaj Sanodiya

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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