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Parallelograms

Parallelograms. Sec: 8.2 Sol: G.8 a, b, c. Quadrilaterals. Are four-sided polygons. What is a polygon? Example: Non – example: Example: Give the possible names of the following figure. Parallelogram.

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Parallelograms

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  1. Parallelograms Sec: 8.2 Sol: G.8 a, b, c

  2. Quadrilaterals Are four-sided polygons. What is a polygon? Example: Non – example: Example: Give the possible names of the following figure.

  3. Parallelogram Is a quadrilateral with both pairs of opposite sides parallel. Ex: What are the vertices? Symbol: ABCD *they are labeled in order as they appear starting with one vertice.

  4. Properties of Parallelograms Theorem 8-3 : Opposite sides of a parallelogram are congruent. Ex: Theorem 8-4 : Opposite angles in a parallelogram are congruent. If AD = 16, BC=_______ If AB = 25, DC = _______ If the mA = 100, then m C = _____ If the mD = 80, then mB = ______

  5. Theorem 8-5 : Consecutive angles in a parallelogram are supplementary. Theorem 8-6 : If a parallelogram has one right angle, it has four right angles. If mA = 120, then mB =_________ If mA = 120, then mC =_________ If mC = 120, then mD =_________ mA = 90 mB= 90 mC = 90 mD = 90

  6. Theorem 8-7 : Diagonals of a parallelogram: The diagonals of a parallelogram bisect each other. Meaning the intersection of the two diagonals is the midpoint of each diagonal. Theorem 8-8 : Each Diagonal of a parallelogram separates the parallelogram into two congruent triangles. M If AM = 16, MC = ___ If DM = 25, MB = ___ If AC = 30, MC = ___

  7. Example: • MATH is a parallelogram. Find w, x, y and z. w° y° 55° z°

  8. Example: 2. Solve for w, x, y, and z. 3x - 4 33° 4w - 3 15.4 17.9 2y + 5 11.1 3z – 3 38° 20

  9. Example: 3. Parallelogram STOP has diagonals , that intersect at point M. If SM = 3a + 18, SO = 12a, MT = a+2b, MP = 3b + 1. Find a. b. and TP.

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