ΔABC and ΔDEF are two triangles such that ΔABC ≅ ΔFDE. If AB = 5 cm, ∠B = 40° and ∠A = 80°, then which of the following options is true?

DF = 5 cm, ∠E = 60°

Concept Used

Congruency of triangle = If a triangle is congruent to another triangle then angle or side must be equal to the same triangle.

Sum of angles of triangle = \({180}^\circ\)

Calculation

According to the question,

\(\Delta \)ABC is congruent to \(\Delta \)FDE

= AB = FD

= BC = DE

= CA = EF

= \(\angle\)A = \(\angle\)F = \({80}^\circ\)

= \(\angle\)B = \(\angle\)D = \({40}^\circ\)

= \(\angle\)C = \(\angle\)E

Through the sum of angles,

\({180}^\circ\) = \(\angle\)A + \(\angle\)B + \(\angle\)C

= \({180}^\circ\) = \({80}^\circ\) +\({40}^\circ\) + \(\angle\)C

= \({180}^\circ\) = \({120}^\circ\) + \(\angle\)C

= \(\angle\)C = \({60}^\circ\)

Since, \(\angle\)C = \(\angle\)E the \(\angle\)E = \({60}^\circ\)

Therefore, DF = 5 cm and \(\angle\)E = \({60}^\circ\).