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6.5 Rhombi and Squares

6.5 Rhombi and Squares. Check.3.2 Connect coordinate geometry to geometric figures in the plane (e.g. midpoints, distance formula, slope, and polygons). Spi.3.2 Use coordinate geometry to prove characteristics of polygonal figures.

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6.5 Rhombi and Squares

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  1. 6.5 Rhombi and Squares Check.3.2 Connect coordinate geometry to geometric figures in the plane (e.g. midpoints, distance formula, slope, and polygons). Spi.3.2 Use coordinate geometry to prove characteristics of polygonal figures. Check.4.10 Identify and apply properties and relationships of special figures (e.g., isosceles and equilateral triangles, family of quadrilaterals, polygons, and solids).

  2. Rhombi B A • Rhombus is a quadrilateral with all four sides are congruent. • Rhombus is a parallelogram. • The diagonals of a rhombus are perpendicular. ACBC • Each diagonal of a rhombus bisects a pair of opposite angles. • DAC BAC  DCA  BCA • ADB CBD  ADB  CDB C D Wisdom is the reward you get for a lifetime of listening when you'd have preferred to talk. Doug Larson

  3. Square A B C D • A Square is a Rhombus, with four right angles • Rhombus is a quadrilateral with all four sides are congruent. • Rhombus is a parallelogram. • The diagonals of a rhombus are perpendicular. ACBC • Each diagonal of a rhombus bisects a pair of opposite angles. • DAC BAC  DCA  BCA = 45 • ADB CBD  ADB  CDB = 45

  4. Measures of a Rhombus • Use Rhombus QRST and the given information to find the value of each variable • Find y if m3 = y2 -31 • m3 = 90 = y2 -31 • 90+31 = y2 • 121 = y2 • √121 = y • y = +/- 11 Find mTQS if mRST =56 mTQR  mRST =56 mTQS = ½ mTQR = 28

  5. Measures of a Rhombus • Use Rhombus LMNP and the given information to find the value of each variable • Find y if m1 = y2 - 54 • m3 = 90 = y2 - 54 • 90+54 = y2 • 144 = y2 • √144 = y • y = +/- 12 Find mPNL if mMLP =64 mTQR  mRST =64 mTQS = ½ mTQR = 32

  6. Determine if the following is a Rhombus, a rectangle, or a square Is ABDC? Is ADCD? Opp Inv slopes Slope AD = -4/2 = -2 Slope CD = 2/4 =1/2

  7. Application The infield is a square. Is the pitcher’s mound located in the center? Diagonals should be equal and bisect each other. ½ (127 ft and 3 3/8 in) = 63 ft 7 11/16 inches Not in the middle

  8. Application A square table has four legs that are 2 feet apart. The table is place over an umbrella stand so that the hole in the center of the table lines up with the hole in the stand. How far away from a leg is the center of the hole? Diagonals should be equal and bisect each other. x√2=2√2=2.82 ½ (2.82) = about 1.4 45 x√2 ? feet 2 feet

  9. Summary • A Square is a Rhombus with 4 right angles • A Rhombus is a quadrilateral with all four sides are congruent. • Rhombus is a parallelogram. • The diagonals of a rhombus are perpendicular. ACBC • Each diagonal of a rhombus bisects a pair of opposite angles. • DAC BAC  DCA  BCA • ADB CBD  ADB  CDB • Practice Assignment • Page 431, 8 - 20 Even

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