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Geometry 6.5

Geometry 6.5. Conditions for Special Parallelograms. Learning Targets. Students should be able to… Prove that a given quadrilateral is a rectangle, rhombus or square. Warm-up. Find the slope of the line passing through the given points. 1 . (3, 5) and (7, 1) 2 . (-2, -2) and (0, 0)

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Geometry 6.5

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  1. Geometry 6.5 Conditions for Special Parallelograms

  2. Learning Targets • Students should be able to… • Prove that a given quadrilateral is a rectangle, rhombus or square.

  3. Warm-up Find the slope of the line passing through the given points. 1. (3, 5) and (7, 1) 2. (-2, -2) and (0, 0) Find the AB for A(-3, 5) and B(1, 2). **Use the distance formula.

  4. Homework Check

  5. Homework Check

  6. Homework Check

  7. 6-5 Theorem

  8. 6-5 Theorem

  9. 6-5 Theorem

  10. 6-5 Theorem

  11. 6-5 Theorem

  12. 6-5 Theorems

  13. Leave this chart. We will come back to this once we have made a few more flow charts.

  14. Properties • Draw pictures on board for visuals if students need. Page 408b in teacher book. • Has four right angles • Properties of a parallelogram • Congruent diagonals • Four congruent sides • Properties of a parallelogram • Perpendicular diagonals • Diagonals bisect opposite angles • All properties of a rectangle • All properties of a rhombus

  15. Quadrilateral Flow Chart If a parallelogram has Congruent diagonals One right angle One pair of congruent consecutive sides One diagonal that bisects a pair of opposite angles Perpendicular diagonals then it is a rectangle then it is a rhombus then it is a square

  16. Finding the correct Quadrilateral. rectangle rhombus square rectangle square rhombus rhombus

  17. Quadrilateral Summary Sheet • Parallelograms have… • Opposite sides congruent. • Opposite angles congruent. • Opposite sides parallel. • Consecutive angles are supplementary. • Diagonals bisect each other. • One pair of opposite sides are congruent and parallel.

  18. Quadrilateral Summary Sheet • Rhombus… • Parallelogram with 4 congruent sides. • Diagonals are perpendicular. • Each diagonal bisects a pair of opposite angles.

  19. Quadrilateral Summary Sheet • Rectangle • Parallelogram with 4 right angles. • Diagonals are congruent.

  20. Quadrilateral Summary Sheet • Square • Parallelogram with 4 congruent sides (rhombus) and 4right angles (rectangle).

  21. Re-teach WS

  22. Re-teach WS

  23. Reteach WS Step 1: Use Distance Formula to see if diagonals are congruent. Step 2: Use Slopes to see if diagonals are perpendicular. Step 3: Use this information to decide what type of parallelogram a figure is. **This will be on the test in the form of Extra Credit.

  24. Re-teach WS • Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all most specific name. 1. V(3, 0), W(6, 4), X(11, 4), Y(8, 0)

  25. Re-teach WS • Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all most specific name. 2. L(1, 2), M(3, 5), N(6, 3), P(4, 0)

  26. Re-teach WS • Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all most specific name. 3. H(1, 3), J(10, 6), K(12, 0), L(3, -3)

  27. Re-teach WS • Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all most specific name. 4. E(-4, 3), F(-1, 2), G(-2, -1), H(-5, 0)

  28. Homework • Page 422 #9-16

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