Question 1174792: Question: Which Of The Following Uses The Given Set Of Points To Prove That ABC A EFD? A(0,0), B (3.0), C(2,3), D(3.0), E (1,3), F (4,3) AB = EF = 761, BC = FD = 34, CA = DE = 5, And ABC AEFD By SAS. AB = EF = V13, BC = FD = V10, CA = DE = 3, And A ABC AEFD By SSS. AB = EF = 9, BC = FD = 10, CA = DE = 13, And ABC > EFD By SAS «
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's calculate the side lengths of triangles ABC and EFD to determine which congruence criterion applies.
**Triangle ABC:**
* AB = √((3 - 0)² + (0 - 0)²) = √(3² + 0²) = √9 = 3
* BC = √((2 - 3)² + (3 - 0)²) = √((-1)² + 3²) = √(1 + 9) = √10
* CA = √((0 - 2)² + (0 - 3)²) = √((-2)² + (-3)²) = √(4 + 9) = √13
**Triangle EFD:**
* EF = √((4 - 1)² + (3 - 3)²) = √(3² + 0²) = √9 = 3
* FD = √((3 - 4)² + (0 - 3)²) = √((-1)² + (-3)²) = √(1 + 9) = √10
* DE = √((1 - 3)² + (3 - 0)²) = √((-2)² + 3²) = √(4 + 9) = √13
**Comparison:**
* AB = EF = 3
* BC = FD = √10
* CA = DE = √13
Since all three sides of triangle ABC are congruent to the corresponding sides of triangle EFD, we can conclude that the triangles are congruent by the Side-Side-Side (SSS) criterion.
Therefore, the correct statement is:
* AB = EF = 3, BC = FD = √10, CA = DE = √13, and ∆ABC ≅ ∆EFD by SSS.
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