Place the trapezoid in the coordinate plane so that one base is on the x-axis.
See solution.
Practice makes perfect
We are asked to prove that the diagonals of an isosceles trapezoid are congruent.
We are asked to use a coordinate proof, so let's place the trapezoid in the coordinate plane so that one base is on the x-axis and one vertex is at the origin.
Since side BC is parallel to the x-axis, the y-coordinates of B and C are the same.
We are asked to investigate the length of the diagonals, so let's recall the Distance Formula.
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 to express the length of the legs of the trapezoid.
Points
Substitution
Length
A(0,0) and B(b,p)
sqrt((b-0)^2+(p-0)^2)
AB=sqrt(b^2+p^2)
C(c,p) and D(d,0)
sqrt((d-c)^2+(0-p)^2)
CD=sqrt((d-c)^2+p^2)
Since the trapezoid is isosceles, we know that AB=CD.
Let's substitute the expression from the table and simplify the resulting equation.
