Question

Which of the following pairs of triangles are congruent ? In each case, state the condition of congruency:

(1) In $\Delta$ ABC and $\Delta$ DEF, AB=DE, BC= EF and $\angle$ B = $\angle$ E.

(2) In $\Delta$ ABC and $\Delta$ DEF, $\angle$ B = $\angle$ E = ${90}^0$, AC =DF and BC = EF.

Answer 1

(1) In $\Delta$ ABC and $\Delta$ DEF,
AB = DE,
BC = EF
and $\angle$ B = $\angle$ E.
By side angle side theorem triangles are congruent.

(2) In $\Delta$ ABC and $\Delta$ DEF,
$\angle$ B = $\angle$ E = ${90}^{\circ }$
AC = DF
and BC = EF.
By Right angle hypotenuse side theorem triangles are congruent.