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Prove Yourself!

Prove Yourself!. Do the following for your “Exercise Your Quads” project…. Parallelograms Rectangles Rhombi Squares Trapezoids. A parallelogram is a quadrilateral with 2 pairs of parallel, congruent sides. Prove it! How can you prove that a parallelogram is actually a parallelogram?.

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Prove Yourself!

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  1. Prove Yourself! Do the following for your “Exercise Your Quads” project… Parallelograms Rectangles Rhombi Squares Trapezoids

  2. A parallelogram is a quadrilateral with 2 pairs of parallel, congruent sides. Prove it! How can you prove that a parallelogram is actually a parallelogram? Draw your parallelogram on graph paper. Prove that opposite sides are parallel by calculating the slopes of each of the sides. Prove that opposite sides are congruent by calculating the length of each of the sides.

  3. A rectangle is a parallelogram that has four right angles. How can you prove that a rectangle is a rectangle? Draw your rectangle on graph paper. Prove that opposite sides are parallel and that adjacent sides are perpendicular by calculating the slopes of each side. Prove that opposite sides are congruent by calculating the length of each side.

  4. A rhombus is a parallelogram that has 4 congruent sides. How can you prove that a rhombus is a rhombus? Draw a rhombus on graph paper and prove that opposite sides are parallel and that all sides are congruent.

  5. A square is a parallelogram that has four right angles and four congruent sides. How can you prove a square is a square? Draw a square on graph paper and prove that it is a square.

  6. A trapezoid has only one pair of parallel sides. Draw a trapezoid on graph paper and prove that it has only one pair of parallel sides, not two pair.

  7. List the definitions and properties for each of the four parallelograms. List the definition of a trapezoid, and list the definition and properties of an isosceles trapezoid.

  8. Example proof for a parallelogram: C D B A The slope of AD = 4 and the slope of BC = 4. Therefore, AD BC. The slope of AB = 2/5 and the slope of DC = 2/5. Therefore, AB DC. The length of AD = 4.123 and the length of BC = 4.123. Therefore, AD = BC. The length of AB = 5.385 and the length of DC = 5.385. Therefore, AB = DC. Since opposite sides are parallel and congruent, then ABCD is a parallelogram.

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