Question

Which of the following uses the given set of points to prove that △ABC ≅ △EFD? Points: A(0,0), B(3,0), C(2,3), D(3,0), E(1,3), F(4,3)

a) Side-Side-Side (SSS)
b) Angle-Angle-Side (AAS)
c) Side-Angle-Side (SAS)
d) Angle-Side-Angle (ASA)

Answer 1

Triangles △ABC and △EFD are congruent by the Side-Side-Side (SSS) postulate because all three pairs of their corresponding sides are equal in length.

Step-by-step explanation:

The question asks which geometric principle can be used to prove that triangles △ABC and △EFD are congruent given the set of points A(0,0), B(3,0), C(2,3), D(3,0), E(1,3), F(4,3). To determine congruence, we need to consider the lengths of sides and measures of angles. By calculating distances between points:

• AB (using A and B): √[(3-0)^2 + (0-0)^2] = √9 = 3 units
• AC (using A and C): √[(2-0)^2 + (3-0)^2] = √(4+9) = √13 units
• BC (using B and C): √[(2-3)^2 + (3-0)^2] = √(1+9) = √10 units
• EF (using E and F): √[(4-1)^2 + (3-3)^2] = √9 = 3 units
• ED (using E and D): √[(3-1)^2 + (0-3)^2] = √(4+9) = √13 units
• FD (using F and D): √[(3-4)^2 + (0-3)^2] = √(1+9) = √10 units

It's evident that AB = EF, AC = ED, and BC = FD. All corresponding sides are equal in length, so we can say that the two triangles are congruent by Side-Side-Side (SSS) postulate, as all three pairs of their corresponding sides are equal.