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?
Answer & explanation
Correct answer: option 1
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 = \({60}^\circ\).