We are asked how the coordinate plane can help us determine that corresponding sides of two figures are congruent. Two sides are congruent if they have an equal length. The sides of a figure are segments, so let's consider two example segments.
We want to verify whether the lengths of the two segments are equal. Since the segments are in a coordinate plane, we can find the coordinates of their endpoints.
Now we can use the distance formula to find the lengths of both segments. Let's recall the distance formula for finding the distance d between two points with coordinates ( x_1, y_1) and ( x_2, y_2).
d = sqrt(( x_2- x_1)^2 + ( y_2- y_1)^2)
Let's find the length of AB! The length is the distance between the endpoints of the segment.
Once again, it does not make sense for a segment to have a negative length, so the length of CD is 5. Since AB and CD have equal lengths, they are congruent!
AB ≅ CD
The coordinate plane allows us to use the distance formula to find the lengths of segments. This allows us to determine whether the corresponding sides of two figures are congruent.
