Coordinate Proof of Isosceles Trapezoid Diagonals
Investigate how positioning an isosceles trapezoid symmetrically on the coordinate plane leads to a general proof that its diagonals are congruent.
Tarea 1
Putting It All Together
Answer these open ended questions on your own or with others to form deeper math connections.
Tarea 2
How can we be sure the general algebraic proof holds for all trapezoids?
Tarea 3
Why is it helpful to rotate and translate the trapezoid before attempting a general algebraic proof that the diagonals are congruent?
Tarea 4
How could you show algebraically that the diagonals of a rectangle are congruent?
Tarea 5
John claims that if you take the midpoints of all the sides of any isosceles trapezoid and join them together, the resulting figure will be a parallelogram. What steps would he need to take to prove this claim using algebra? How could you prove it using geometry?