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6.4 Special Parallelogram 2 .notebook December 08, 2014 DIRT 1. Solve for the variable: b. 4(2y+1) = 20 a. 8x3=6x+5 2. Rewrite the following equation in slope intercept form: 2y + 7 = x 3. What does it mean if two lines are perpendicular? Explain using words. Then, draw and label a picture of two perpendicular lines. Dec 87:57 AM Jan 147:16 AM 6.4 Special Parallelograms Objectives: To use properties of diagonals of rhombus or rectangle To determine whether a parallelogram is a rhombus, or a rectangle 2 ways to prove that a parallelogram is a RECTANGLE: 1) One right angle in the corner Review: 2) Diagonals are congruent 5 ways to prove that a quadrilateral is a parallelogram: 1) Opposite sides are parallel 2 ways to prove that a parallelogram is a RHOMBUS: 2) Opposite sides are congruent 1) Consecutive sides are congruent 3) Opposite angles are congruent 2) Diagonals are perpendicular (Rt angle in the middle) 4) Diagonals bisect each other *****The diagonals of a rhombus bisect the angles****** 5) One set of sides are both parallel and congruent Jan 147:18 AM Rhombus equilateral parallelogramall properties of a parallelogram apply and 1) All 4 sides are congruent 2) Diagonals are perpendicular bisectors 3) Each diagonal bisects 2 angles Jan 147:22 AM 3) 4y 2x 20 Code and label the picture 16 4) Examples: Find the measures of the numbered angles in each rhombus (code and label the pictures) 2y2 3x+1 120 14 10 1) 120 3 1 2 4 5 5) 2) 50 4 1 2 3 Jan 147:23 AM Jan 147:26 AM 1 6.4 Special Parallelogram 2 .notebook One diagonal of a rectangle has length 8x + 2. The other diagonal has length 5x + 11. Find the length of each diagonal December 08, 2014 Assignment: p 315 #28E, 4547, 49, 50, 5758, 6769 2. Draw picture and label: 4. Draw picture and label: work: work: m<1=______ m<2=_______ m<3=_______ m<1=_______ m<2=________ m<3=________ m<4=________ The diagonals of ABCD are perpendicular. AB = 16 cm and BC = 8 cm. Can ABCD be a parallelogram? Explain. 6. Draw picture and label: 8. Draw picture and label: work: work: m<1=_______ m<2=________ m<1=______ m<2=______ m<3=______ m<3=________ m<4=_______ 45. Good definition? _______ Why/Why not?_______________________________ 46. Good definition? _______ Why/Why not?_______________________________ 47. Good definition? _______ Why/Why not?_______________________________ Jan 147:27 AM Jan 1410:26 AM 49. Draw picture and label: 50. Draw picture and label: work: work: x = _____ y = _____ z = _____ x = _____ y = _____ 57. Draw picture and label: 58. Draw picture and label: work: work: AC= ________ BD= __________ 67. Draw picture: DB= ________ AC= ______ 68. Draw picture: 69. Draw picture: Parallelogram? _______ Parallelogram? _______ Parallelogram? ______ Why/Why not?___________ Why/Why not?___________ Why/Why not?___________ _______________________ _______________________ ______________________ _______________________ _______________________ ______________________ Jan 1410:30 AM 2