Let's think about the relationship between the coordinates of P, Q, R, and S.
Vertex Q is on the y-axis, so the x-coordinate is 0.
Vertex S is on the x-axis, so the y-coordinate is 0.
Side RS is parallel to the y-axis, so the x-coordinate of R and S are the same.
Side QR is parallel to the x-axis, so the y-coordinate of Q and R are the same.
Let's use variables to name the coordinates of Q, R, and S.
These are just example variables, so your variable choices may differ.
c
It is given that PQRS is a rectangle, and the claim is that the diagonals are congruent.
2
&Given:&& PQRS is a rectangle
&Prove:&& PR≅QS
d
To show that two segments are congruent, it is enough to show that they have the same lengths. In a coordinate proof we can use the Distance Formula to express the length of a segment in terms of the coordinates of the endpoints.
The distance
between points(x_1,y_1)and(x_2,y_2)is
sqrt((x_2-x_1)^2+(y_2-y_1)^2).Let's use this formula first to find the length of diagonal PR.
