Question

triangle ABC is congruent to triangle FDE and AB=6cm, angle B=40 angle A=80 what is length of side DF of triangle FDE and angle E?

Answer 1

GIVEN

Triangle ABC is congruent to triangle FDE

AB = 6 cm

$\sf{ \angle \: B = {40}^{ \circ} \: \: \: and \: \: \: \angle \: A = {80}^{ \circ} }$

TO DETERMINE

1. The length of side DF of triangle FDE

$\sf{ 2. \: \: \angle E }$

CONCEPT TO BE IMPLEMENTED

If two triangles are congruent then the corresponding sides are equal in length and the corresponding angles are equal in size for the two triangles

CALCULATION

We know that Sum of the three angles in a triangle is 180°

Hence

$\sf{ \angle \: A +\angle \: B + \angle \: C = {180}^{ \circ} }$

$\implies \sf{ {80}^{ \circ} + {40}^{ \circ} + \angle \: C = {180}^{ \circ} }$

$\implies \sf{ \angle \: C = {60}^{ \circ} }$

Since triangle ABC is congruent to triangle FDE

So the corresponding sides are equal in length and the corresponding angles are equal in size for the two triangles ABC and FDE

$\therefore \: \: \sf{ \angle \: E = \angle C \: = {60}^{ \circ} }$

$\sf{DF = AB = 6 \: cm}$

RESULT

$\boxed{ \: \: \: \sf{ \angle \: E = {60}^{ \circ} } \: \: and \: \: \: \: DF = 6 \: cm \: \: \: \: }$

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