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Warm-up 2/8/12

Warm-up 2/8/12. Determine whether PQRS is a Rhombus. 1. P(1,2) Q(3,5) R(1,8) S(-1,5). YES. 1 st : Parallelogram b/c both pairs opp. sides ||. 2 nd : Rhombus b/c diagonals are . Homework Answers Rhombi. ST = 9,VT = 9,RV = 9 VS = 14 RX = 6 20.8 ft (4 – 2)180 = 2(180) = 360

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Warm-up 2/8/12

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  1. Warm-up 2/8/12 Determine whether PQRS is a Rhombus. 1. P(1,2) Q(3,5) R(1,8) S(-1,5) YES 1st: Parallelogram b/c both pairs opp. sides || 2nd: Rhombus b/c diagonals are 

  2. Homework Answers Rhombi • ST = 9,VT = 9,RV = 9 • VS = 14 • RX = 6 • 20.8 ft • (4 – 2)180 = 2(180) = 360 • 2(x – 5) = 90 x = 50 • 2x + 12 = 8x – 20 x = • 5x = 60 x = 12 • 5x + 30 = 180 x = 30

  3. 15. A ( 0, 0) B ( 4, -3) C ( 8, 0) D (4, 3) Distance of edges: AB = 5, AD = 5, CD = 5, BC = 5 Distance of diagonals: AC = 8, BD = 6 (diagonals are not congruent) ABCD is a rhombus, because all sides are congruent. • A = (12)(10) = 120 • A = ½(21)(11) = 115.5 • A = (12)(5) = 60 • A = ½(10)(4) = 20

  4. 4.6 Square Essential Questions: (1). What are the characteristics of a square? (2). How can we prove a polygon is a square?

  5. Essential Question #1 What are the characteristics of a square?

  6. A quadrilateral with four congruent sides and four right angles. Define Square: Since all of the angles in a square are right angles, all squares are ______________. rectangles Since all the edges in a square are congruent, all squares are ______________. rhombi

  7. The properties of rectangles and rhombuses (rhombi) also pertain to squares: • Opposite edges of a square are ________ and __________. • Opposite angles of a square are _________. • Consecutive interior angles of a square are______________. • The diagonals of a square __________each other. parallel congruent congruent supplementary bisect

  8. The properties of rectangles and rhombuses (rhombi) also pertain to squares: • The diagonals of a square are __________ and _____________. • The diagonals of a square __________ opposite angles of the square. • All four edges of a square are _____________. • All four angles of a square are ____________. congruent perpendicular bisect congruent right angles

  9. X W Y Z A Answer each question using square XWZY pictured above. (1). If XW = 5cm, then WZ = ____ , YZ = ____ and XY = _____. (2). 5cm 5cm 5cm 90o 90o 90o

  10. X W Y Z A (3). If XA = 9 in., then YA = _____ , WA = _____, XZ = _____, and WY = ______. (4). mXAY = ______º, mYXA = ______º (5). XW ║ _____; XY ║______. 9 in. 9 in. 18 in. 18 in. 90 45 WZ YZ

  11. X W Y Z A (6). XW ______; XW _______. (7). WY _______ (8). XZ bisects _____ and ______. WZ  XY   XZ Z X

  12. X W Y Z A (9). If XW = 10 ft then the perimeter of the square is _____ ft. 40 (10). The sum of the measures of the interior angles of the square is _____°. 360

  13. (11). Is the square a quadrilateral? (12). Is the square a parallelogram? T T (13). Is the square a rectangle? (14). Is the square a rhombus? T T

  14. http://wrir4.ucdavis.edu/PHOTOS/CROPS/images/Lettuce%20WideBeds.jpghttp://wrir4.ucdavis.edu/PHOTOS/CROPS/images/Lettuce%20WideBeds.jpg . . put our heads together to…. Answer Essential Question #1 What are the characteristics of a square? Chart

  15. Essential Question #2 How can we prove a polygon is a square?

  16. How to prove a quadrilateral is a Square: Prove it is both a ____________________ and a ___________________ Rectangle Rhombus

  17. What is the most specific name for the following Quadrilaterals? rectangle parallelogram (16). ___________ (15). _____________ (18). _____________ parallelogram (17). _____________ rhombus

  18. What is the most specific name for the following Quadrilaterals? (19). _____________ rhombus (20). _____________ quadrilateral rectangle rectangle (21). _____________ (22). _____________

  19. Prove that Quadrilateral WXYZ is a square:W(10,6), X(6,10), Y(10,14), Z(14,10) WX // YZ and XY // WZ because they have equal slopes. Therefore, WXYZ is a parallelogram because both pairs of opposite sides are parallel, WX ┴ XY which means the corner is a right angle , so WXYZ is a rectangle. WY ┴ XZ because one is vertical and the other is horizontal Therefore, WXYZ is a Rhombus Since WXYZ is both a rectangle and a rhombus Then WXYZ is a SQUARE!

  20. http://wrir4.ucdavis.edu/PHOTOS/CROPS/images/Lettuce%20WideBeds.jpghttp://wrir4.ucdavis.edu/PHOTOS/CROPS/images/Lettuce%20WideBeds.jpg . . put our heads together to…. Answer Essential Question #2 How can we prove a polygon is a square? Chart

  21. Area Classwork • 81 • 35 • 72 • 96 • 6 • 16.56

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