How can you prove line congruence?

Question

The problem gives you four points: (9,1), (3,5), (7,11), and (13, 7). It asks to show the diagonals of the figure are congruent. 

Answer 1

Lines can't be congruent because they extend infinitely. You want to show the segments are congruent.

One diagonal has endpoints (3,5) and (13,7).

Use the distance formula to find its length.

d = √[(x₂ - x₁)² +(y₂ - y₁)²]

d = √[(13-3)² + (7-5)²] = √(10² + 2²) = √104 = 2√26

 

The other diagonal has endpoints (7,11) and (9,1).

d = √[(9-7)² + (1-11)²] = √[(2²) + (-10)²] = √104 = 2√26