Question : If it is given that for two right-angled triangles $\triangle$ABC and $\triangle$DFE, $\angle$A = 25°, $\angle$E = 25°, $\angle$B = $\angle$F = 90°, and AC = ED, then which one of the following is TRUE?
Option 1: $\triangle \mathrm{ABC} \cong \triangle \mathrm{FED}$
Option 2: $\triangle \mathrm{ABC} \cong \triangle \mathrm{DFE}$
Option 3: $\triangle \mathrm{ABC} \cong \triangle \mathrm{EFD}$
Option 4: $\triangle \mathrm{ABC} \cong \triangle \mathrm{DEF}$
Correct Answer: $\triangle \mathrm{ABC} \cong \triangle \mathrm{EFD}$
Solution :
Two right-angled triangles are said to be congruent to each other when the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right-angled triangle.
As, $\angle$A = $\angle$E = 25°, $\angle$B = $\angle$F = 90°, and AC = ED
According to the congruence theorem of the triangle, it can be written as $\triangle \mathrm{ABC} \cong \triangle \mathrm{EFD}$
Thus, $\angle$A = $\angle$E; $\angle$B = $\angle$F; $\angle$C =$\angle$D
Hence, the correct answer is $\triangle \mathrm{ABC} \cong \triangle \mathrm{EFD}$.
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