Coordinate Proof of Isosceles Trapezoid Diagonals
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.
Putting It All Together
Answer these open ended questions on your own or with others to form deeper math connections.
Open-ended question 1
How can we be sure the general algebraic proof holds for all trapezoids?
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Open-ended question 2
Why is it helpful to rotate and translate the trapezoid before attempting a general algebraic proof that the diagonals are congruent?
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Open-ended question 3
How could you show algebraically that the diagonals of a rectangle are congruent?
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Open-ended question 4
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?
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Prerequisite Resources
More from Plane Figures on the Coordinate Plane
