07+-+Coordinate+Proofs

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The interactives below correspond to the take-home quiz you were given in class. A copy is attached here:

Choose your own problems and use the interactives to get a better understanding of what is being asked as well as the characteristics of the shape at the center of the proof. Drag them around. Test your ideas. See if you can see why the hypothesis you're tasked to prove is true (they're all true). Then -- as in the PowerPoint above -- try to create the proof.

Pick any of the problems below. Prove the theorem for the proof for full credit. Your total score cannot exceed the sum of the scores for the problems chosen. You can earn up to (but no more than) 110 points.

1. (10 points) Prove that the medians to the legs of an isosceles triangle are equal in length.

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3. (20 points) Prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and has length half that of the third side.

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5. (30 points) Prove that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. How does this result show that any parallelogram can be represented by figure (c) of Class Exercise 2?

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7. (25 points) Prove that the lengths of the diagonals of an isosceles trapezoid are equal

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9. (40 points) Prove that the line segments joining the midpoints of successive sides of any quadrilateral form a parallelogram.

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11. (50 points) Prove that if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

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