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Geometry 6.4

Geometry 6.4. Properties of Special Parallelograms. Learning Targets. Students should be able to… Prove and apply properties of rectangles, rhombuses, and squares. Use properties of rectangles, rhombuses, and squares to solve problems. Warm-up. 6.1 – 6.3. Clear desks.

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Geometry 6.4

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  1. Geometry 6.4 Properties of Special Parallelograms

  2. Learning Targets • Students should be able to… • Prove and apply properties of rectangles, rhombuses, and squares. • Use properties of rectangles, rhombuses, and squares to solve problems.

  3. Warm-up

  4. 6.1 – 6.3 • Clear desks. • It is now time to take the quiz.

  5. Vocabulary B C A D

  6. Vocabulary B C A D C B A D

  7. Vocabulary B C A D C B A D C B A D

  8. Venn Diagram • Here is a Venn Diagram for the information today. We will be adding to this and recording it in our Quadrilateral Summary Sheet. P A R A L L E L O G R A M S q u a r e Rectangle Rhombus

  9. Always, Sometimes, or Never a. A rhombus is a rectangle. b. A parallelogram is a rectangle. c. A square is a rhombus d. A rhombus is a parallelogram

  10. Properties of Rectangles

  11. Properties of Rhombuses

  12. Properties of Squares • A square has the features of both rhombuses and rectangles!! Parallelogram Rectangle Rhombus Square

  13. Example • If ABCD is a rectangle, what do you know about ABCD? • 4 right angles (by definition of rectangle) • Opposite sides are congruent and parallel (definition of parallelogram) • Opposite angles are congruent (since parallelogram) • Consecutive angles are supplementary (since parallelogram) • Diagonals bisect each other. (since parallelogram)

  14. Corollaries about Special Quadrilaterals • Rhombus: • A quadrilateral is a rhombus if and only if it has four congruent sides. • Rectangle: • A quadrilateral is a rectangle if and only if it has four right angles. • Square: • A quadrilateral is a square if and only if it is a rhombus and a rectangle.

  15. Time To Use The Theorems • Ex: PQRS is a rhombus. If PS = 2y + 3 and SR = 5y – 6, what is the value of y?

  16. Time To Use The Theorems • Example: RSTV is a rhombus. Find VT

  17. Time To Use The Theorems • Example: RSTV is a rhombus. Find (y+2) (2y+10)

  18. Your Turn! Try on your own! Ex: In rectangle ABCD, if AB = 7x – 3 and CD = 4x + 9, then find the value of x. (a) 1 (b) 2 (c) 3 (d) 4 (e) 5

  19. Verifying Properties of Squares • You must show that the diagonals of square ABCD are congruent perpendicular bisectors of each other. A(-1, 0), B(-3, 5), C(2, 7), D(4, 2).

  20. Verifying Properties of Squares • You must show that the diagonals of square ABCD are congruent perpendicular bisectors of each other. A(-1, 0), B(-3, 5), C(2, 7), D(4, 2).

  21. Verifying Properties of Squares • You must show that the diagonals of square ABCD are congruent perpendicular bisectors of each other. A(-1, 0), B(-3, 5), C(2, 7), D(4, 2).

  22. Verifying Properties of Squares • You must show that the diagonals of square ABCD are congruent perpendicular bisectors of each other. A(-1, 0), B(-3, 5), C(2, 7), D(4, 2).

  23. Verifying Properties of Squares • Another Try! If needed on one sheet of paper.

  24. Practice B

  25. Practice B

  26. Practice B

  27. Extra Practice

  28. Extra Practice

  29. Extra Practice

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