Best solutions to - "Decide whether enough information is given to prove..."

lwfrgin

Answered question

2020-12-16

Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.

Answer & Explanation

Brittany Patton

Skilled2020-12-17Added 100 answers

We have

By using sum of interior angle property in $△ A B C and △ D E F$ ,
$∠ A B C = 180^{\circ} - (∠ A B C + ∠ B A C)$
$∠ D E F = 180^{\circ} - (∠ E D F + ∠ D F E)$ , so
$∠ A C B = ∠ E D F = 90^{\circ}$ (given)...(i)
$∠ B A C = ∠ D F E (g i v e n)$ ...(ii)
Adding equation (i) and (ii) and subtracting them form $180^{\circ}$ in both sides,
$180^{\circ} - (∠ A C B + ∠ B A C) = 180^{\circ} - (∠ E D F + ∠ D F E)$
$∠ A B C = ∠ D E F$
Now, in $△ A B C and △ D E F$ ,
AB=EF(given)
$∠ A B C = ∠ D E F$ (Proved above)
BC=DE(given)
$△ A B C \tilde{=} △ D E F$ (By SAS Congruence Theorem)

So
Yes, the provided information is enough to prove the triangle congruent by SAS.

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