Question

Multi-Step Use the given set of points to prove each congruence statement.

A(2,3),
B(4,1),
C(1,-1),
D(-1,0),
E(-3,-2),
F(0,-4)

Answer 1

To prove congruence statements, we need to show that the lengths of corresponding segments are equal. However, the lengths of AB and FE are different, so they are not congruent.

Step-by-step explanation:

To prove the congruence statements, we need to show that the lengths of corresponding segments are equal. Let's start with AB and FE:

• The length of AB can be calculated using the distance formula: AB = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((4 - 2)^2 + (1 - 3)^2) = sqrt(2^2 + (-2)^2) = sqrt(4 + 4) = sqrt(8).
• The length of FE can also be calculated using the distance formula: FE = sqrt((-3 - 0)^2 + (-2 - (-4))^2) = sqrt((-3)^2 + (2)^2) = sqrt(9 + 4) = sqrt(13).

Since AB and FE have different lengths, they are not congruent. Therefore, we cannot prove the congruence statement for AB and FE with the given set of points.