Question

If ABC and DEF are two triangles such that $\Delta ABC\cong \Delta FDEandAB=5cm,\angle B={40}^{\circ }and\angle A={80}^{\circ }.$ Then, which of the following is true?

• A. DF = 5 cm, $\angle F={60}^{\circ }$
• B. DE = 5 cm, $\angle E={60}^{\circ }$
• C. DF = 5 cm, $\angle E={60}^{\circ }$
• D. DE = 5 cm, $\angle D={40}^{\circ }$

Answer 1

The correct option is C

DF = 5 cm, $\angle E={60}^{\circ }$

(c),

$\because \Delta ABC\cong \Delta FDE,$

$AB=5cm,\angle A={80}^{\circ },\angle B={40}^{\circ }$

$\therefore DF=5cm,\angle F={80}^{\circ },\angle D={40}^{\circ }$

$\therefore \angle C={180}^{\circ }-({80}^{\circ }+{40}^{\circ })={180}^{\circ }={120}^{\circ }={60}^{\circ }$

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

$\therefore DF=5cm,\angle E={60}^{\circ }$