Question

What additional information would you need to prove that ΔABC ≅ ΔDEF by SSS?

A) The lengths of all three sides of both triangles.
B) The measures of all three angles of both triangles.
C) The measures of two angles and the length of the included side of both triangles.
D) The measures of two angles and the lengths of the two adjacent sides of both triangles.

Answer 1

To prove triangle congruence by SSS, the lengths of all three sides of both triangles are needed. The correct answer is therefore A) The lengths of all three sides of both triangles.

Step-by-step explanation:

To prove that two triangles are congruent using the Side-Side-Side (SSS) congruence theorem, you need the lengths of all three sides of both triangles. According to the question, the correct choice would be A) The lengths of all three sides of both triangles. This is because SSS congruence criterion states that if all three sides of one triangle are equal in length to the corresponding sides of another triangle, the two triangles are congruent.

The Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b), is applicable for right triangles and can help calculate side lengths if the triangles are right-angled. However, SSS congruence does not specifically require the triangles to be right-angled.