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Review for Parallelogram Properties Quiz

Review for Parallelogram Properties Quiz. G.GPE.B.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle. Warm-up .

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Review for Parallelogram Properties Quiz

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  1. Review for Parallelogram Properties Quiz G.GPE.B.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle.

  2. Warm-up • Show that A(2, -1), B(1, 3), C(6, 5), and D(7, 1) are the vertices of a parallelogram.

  3. Method 1 Show that opposite sides have the same slope, so they are parallel.

  4. Method 2 • Show that opposite sides have the same length.

  5. Method 3

  6. Sometimes, Always or Never True Sometimes, if it’s a rectangle. • The diagonals of a parallelogram are congruent. • The consecutive angles of a rectangle are congruent and supplementary. Always • The diagonals of a rectangle bisect each other. Always Sometimes, if it’s a square. • The diagonals of a rectangle bisect the angles. • The diagonals of a square are perpendicular bisectors of each other. Always • A square is a rectangle. Always

  7. Sometimes, Always or Never True • A diagonal divides a square into two isosceles right triangles. Always • Consecutive angles in a parallelogram are congruent Sometimes, if it’s a square or a rectangle. Consecutive angles are always supplementary.

  8. B(1, 5) O(9, 9) X(11, 5) Y(3, 1) • Is BOXY a rectangle? Why? • The diagonals of BOXY are __________________

  9. More Practice!!! 1. D D C C 2. 4x +3 2x - 7 63 x + 9 A A B B Perimeter ABCD = 46 Find the measure of Perimeter ABCD = 16x – 12. Measure of AD =_____________ 16 7 75

  10. READY FOR A CHALLENGE??? Find the coordinates of point M in parallelogram PRAM (b-a, c) M(?, ?) A(b, c) P R(a, 0)

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