1. Geometry Today: Class Attendance / Announcements 6.4 Vocabulary Review Warm-Up 6.4 Notes / Practice Begin Homework Every moment in planning saves 3 or 4 in execution. Crawford Greenwalt

2. 1. 2. 3. 4. 5. WARM-UP What are the properties of a parallelogram? 6.3

3. 6.4 – Rhombuses, Rectangles, & Squares Objectives: 1.Know special parallelograms 2.Know properties of special parallelograms Vocabulary: square, rhombus, rectangle

4. Vocabulary Rectangle – a quadrilateral with 4 right angles 6.4

5. RECTANGLE FACTS: Has all 5 properties of a parallelogram  + Has four right angles. + Diagonals are congruent. + A parallelogram is a rectangle iff the diagonals are congruent. 6.4 7 properties total

6. Vocabulary Rhombus – a quadrilateral with 4 congruent sides 6.4

7. RHOMBUS FACTS: + Diagonals are  + Diagonals bisect angles. A parallelogram is a rhombus iff the diagonals are perpendicular. A parallelogram is a rhombus iff the diagonals bisect the angles. 6.4 Has all 5 properties of a parallelogram  + Has four congruent sides. 8 properties total

8. Vocabulary Square – a quadrilateral with 4 right angles and 4 congruent sides (both a rhombus and a rectangle) 6.4

9. SQUARE FACTS Has all 5 properties of a parallelogram  Has all properties of a rectangle (additional 2 properties). 6.4 10 properties total Has all properties of a rhombus (additional 3 properties).

10. Break Time Take a few minutes to get up, stretch out, or try the following rebus puzzles. To see red Travel overseas

11. Quadrilaterals (4 sides) Parallelograms (opp. sides ll) Rhombus (all sides  ) Rectangles (all right  ’s) Square (Rect & Rhomb) 6.6

12. What type of quadrilateral is ABCD? Parallelogram Rectangle A B C D

13. QUESTIONS ABOUT SPECIAL QUADRILATERALS Answer each question with A, S, N for always, sometimes, and never true. 1.A rectangle is a square  2.A square is a rhombus  3.A rectangle is a parallelogram  4.A rectangle is a rhombus  6.4

14. Propertyllrectrhmsqrkitetrpistrp Both pairs of opposite sides parallel Exactly 1 pair of opposite sides parallel Diagonals perpendicular Diagonals congruent Diagonals bisect each other Both pairs of opposite sides are congruent Exactly one pair of opposite sides are congruent All sides are congruent Both pairs of opposite angles are congruent Exactly one pair of opposite angles are congruent All angles are congruent

15. Propertyllrectrhmsqrkitetrpistrp Both pairs of opposite.sides parallel X Exactly 1 pair of opposite sides parallel Diagonals perpendicular Diagonals congruent Diagonals bisect each other X Both pairs of opposite sides are congruent X Exactly one pair of opposite sides are congruent All sides are congruent Both pairs of opposite angles are congruent X Exactly one pair of opposite angles are congruent All angles are congruent

16. Propertyllrectrhmsqrkitetrpistrp Both pairs of opposite.sides parallel XX Exactly 1 pair of opposite sides parallel Diagonals perpendicular Diagonals congruent X Diagonals bisect each other XX Both pairs of opposite sides are congruent XX Exactly one pair of opposite sides are congruent All sides are congruent Both pairs of opposite angles are congruent XX Exactly one pair of opposite angles are congruent All angles are congruent X

17. Propertyllrectrhmsqrkitetrpistrp Both pairs of opposite.sides parallel XXX Exactly 1 pair of opposite sides parallel Diagonals perpendicular X Diagonals congruent X Diagonals bisect each other XXX Both pairs of opposite sides are congruent XXX Exactly one pair of opposite sides are congruent All sides are congruent X Both pairs of opposite angles are congruent XXX Exactly one pair of opposite angles are congruent All angles are congruent X

18. Propertyllrectrhmsqrkitetrpistrp Both pairs of opposite.sides parallel XXXX Exactly 1 pair of opposite sides parallel Diagonals perpendicular XX Diagonals congruent XX Diagonals bisect each other XXXX Both pairs of opposite sides are congruent XXXX Exactly one pair of opposite sides are congruent All sides are congruent XX Both pairs of opposite angles are congruent XXXX Exactly one pair of opposite angles are congruent All angles are congruent XX

19. QUESTIONS ABOUT SPECIAL QUADRILATERALS List all the special quadrilaterals that have each property: 1.Diagonals are congruent  2.Diagonals are perpendicular  3.Consecutive angles are supplementary. 4.Regular polygon 6.4

20. MNOP is a rectangle with interior point A. If MA = 6x + 4 and PA = 7x – 4, find PN. 6.4

21. A DC B 5x + 8° 3x + 2° 6.4 Find x and y, such that ABCD is a rectangle. 6y + 2°

22. QRST is a rhombus. Find x and y, if m  1 = y 2 – 54, m  2 = 5x + 7 and m  3 = 7x – 1. Q R T S 2 3 6.4 1

23. Is ABCD a square, rectangle or rhombus? D A C B x + 7 3y + 3 6.4 2x – 4 4y – 2 10z + 5° 8z + 13°

24. Geometry Homework: 6.4 pgs. 351-352 #16-38 Chapter 6 Test on Wednesday Chapter 6 Test on Wednesday Every moment in planning saves 3 or 4 in execution. Crawford Greenwalt