Question : If it is given that for two right-angled triangles $ riangle$ABC and $ riangle$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: $ riangle \mathrm{ABC} \cong riangle \mathrm{FED}$
Option 2: $ riangle \mathrm{ABC} \cong riangle \mathrm{DFE}$
Option 3: $ riangle \mathrm{ABC} \cong riangle \mathrm{EFD}$
Option 4: $ riangle \mathrm{ABC} \cong riangle \mathrm{DEF}$

Question

Question : If it is given that for two right-angled triangles $ riangle$ABC and $ riangle$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: $ riangle \mathrm{ABC} \cong riangle \mathrm{FED}$

Option 2: $ riangle \mathrm{ABC} \cong riangle \mathrm{DFE}$

Option 3: $ riangle \mathrm{ABC} \cong riangle \mathrm{EFD}$

Option 4: $ riangle \mathrm{ABC} \cong riangle \mathrm{DEF}$

Team Careers360 · Accepted Answer

Correct Answer: $ riangle \mathrm{ABC} \cong riangle \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 $ riangle \mathrm{ABC} \cong riangle \mathrm{EFD}$
Thus, $\angle$A = $\angle$E; $\angle$B = $\angle$F; $\angle$C =$\angle$D
Hence, the correct answer is $ riangle \mathrm{ABC} \cong riangle \mathrm{EFD}$.

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Question : If it is given that for two right-angled triangles △ABC and △DFE, ∠A = 25°, ∠E = 25°, ∠B = ∠F = 90°, and AC = ED, then which one of the following is TRUE?Option 1: △ABC≅△FEDOption 2: △ABC≅△DFEOption 3: △ABC≅△EFDOption 4: △ABC≅△DEF

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