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Section 9: Rhombuses, Rectangles, and Squares

Section 9: Rhombuses, Rectangles, and Squares. Goals. Use properties of diagonals of rhombuses, rectangles, and squares Use properties of sides and angles of rhombuses, rectangles, and squares. Anchors. Apply appropriate techniques, tools, and formulas to determine measurements.

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Section 9: Rhombuses, Rectangles, and Squares

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  1. Section 9:Rhombuses, Rectangles, and Squares

  2. Goals • Use properties of diagonals of rhombuses, rectangles, and squares • Use properties of sides and angles of rhombuses, rectangles, and squares Anchors • Apply appropriate techniques, tools, and formulas to determine measurements. • Analyze characteristics and properties of two and three dimensional geometric shapes and demonstrate understanding of geometric relationships.

  3. Properties of Special Parallelograms Rhombus • All the properties of a parallelogram • All four sides are congruent • The diagonals are perpendicular • The diagonals bisect the interior angles x y y x 90 90 90 90 x y y x

  4. Properties of Special Parallelograms Rectangle • All the properties of a parallelogram • All sides meet at 90 • Each of the diagonals are congruent A B x x y y AC = BD E y y x x D C Makes two pairs of isosceles triangles. AE = EC = ED = EB

  5. A B D C Properties of Special Parallelograms Square • All the properties of a parallelogram • All the properties of a rhombus • All the properties of a rectangle 45 45 45 45 90 90 90 90 45 45 45 45

  6. Parallelogram Rectangles Squares Rhombuses

  7. Rectangle ABCD ABE = 10x - 5 BCA = 4x – 3 Find all angles. ABE + BCA = 90 10x - 5 + 4x - 3 = 90 X = 7 25 25 65 65 130 50 50 130 65 65 25 25

  8. Rectangle QRST QRU = 4x + 4 RUQ = 15x - 12 Find all angles. 54 54 36 36 72 108 108 72 QRU + RQU + RUQ = 180 36 36 4x + 4 + 4x + 4 + 15x - 12 = 180 54 54 X = 8

  9. 40 50 40 50 90 90 90 90 50 40 50 40 Rhombus PROD PRU = 9x - 4 PDU = 5x + 20 Find all angles. PRU = PDU 9x - 4 = 5x + 20 x = 6

  10. Rhombus JELY UEJ = 2x + 6 YLU = 4x Find all angles. 34 34 56 56 90 90 90 UEJ + YLU = 90 90 2x + 6 + 4x = 90 56 56 x = 14 34 34

  11. What special type of quadrilateral is ABCD? A ( -4 , 7 ) , B ( 6 , 9 ) , C ( 8 , 16 ) D ( -2 , 14 ) How do we do that? What do we need to know? 1 / 5 7 / 2 1 / 5 7 / 2 Length of AB = Length of BC = Length of CD = Length of AD = 2√26 √53 2√26 √53 Slope of AB = Slope of BC = Slope of CD = Slope of AD = ABCD is a parallelogram – b/c it has two sets of parallel and congruent sides.

  12. What special type of quadrilateral is EFGH? E ( 4 , -8 ) , F ( 7 , -3 ) , G ( 12 , -6 ) H ( 9 , -11 ) How do we do that? What do we need to know? 5 / 3 -3 / 5 5 / 3 -3 / 5 Length of AB = Length of BC = Length of CD = Length of AD = √34 √34 √34 √34 Slope of EF = Slope of FG = Slope of GH = Slope of EH = EFGH is a square – b/c it has two sets of parallel sides, all sides are congruent, and the slopes are negative reciprocals.

  13. What special type of quadrilateral is IJKL? I ( -9 , -9 ) , J ( -6 , -2 ) , K ( -3 , -9 ) L ( -6 , -16 ) How do we do that? What do we need to know? 7 / 3 -7 / 3 7 / 3 -7 / 3 Length of IJ = Length of JK = Length of KL = Length of IL = √58 √58 √58 √58 Slope of IJ = Slope of JK = Slope of KL = Slope of IL = IJKL is a rhombus– b/c it has two sets of parallel sides and all sides are congruent, Diagonals are perpendicular. Slope of IK = 0 and slope of JL is undefined.

  14. What special type of quadrilateral is MNOP? M ( 2 , 2 ) , N ( 5 , 11 ) , O ( 14 , 14 ) P ( 11 , 5 ) How do we do that? What do we need to know? 3 1 / 3 3 1 / 3 Length of MN = Length of NO = Length of OP = Length of MP = 3√10 3√10 3√10 3√10 Slope of MN = Slope of NO = Slope of OP = Slope of MP = MNOP is a rhombus– b/c it has two sets of parallel sides and all sides are congruent, Diagonals are perpendicular. Slope of MO = 1 and slope of NP = -1.

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