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Tests for Parallelograms

Tests for Parallelograms. Proving Quadrilaterals as Parallelograms 5 ways. If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram. From definition:. H. G. E. F. Proving Quadrilaterals as Parallelograms. Theorem 1:.

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Tests for Parallelograms

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  1. Tests for Parallelograms

  2. Proving Quadrilaterals as Parallelograms 5 ways If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram . From definition: H G E F

  3. Proving Quadrilaterals as Parallelograms Theorem 1: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram . H G Theorem 2: E F If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram .

  4. Theorem: Theorem 3: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. G H then Quad. EFGH is a parallelogram. M Theorem 4: E F If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram . then Quad. EFGH is a parallelogram. EM = GM and HM = FM

  5. 5 ways to prove that a quadrilateral is a parallelogram. 1. Show that both pairs of opposite sides are || . [definition] 2. Show that both pairs of opposite sides are  . 3. Show that one pair of opposite sides are both  and || . 4. Show that both pairs of opposite angles are  . 5. Show that the diagonals bisect each other .

  6. Examples …… Example 1: Find the value of x and y that ensures the quadrilateral is a parallelogram. y+2 6x = 4x+8 2x = 8 x = 4 units 2y = y+2 y = 2 unit 6x 4x+8 2y Find the value of x and y that ensure the quadrilateral is a parallelogram. Example 2: 5y + 120 = 180 5y = 60 y = 12 units 2x + 8 = 120 2x = 112 x = 56 units (2x + 8)° 120° 5y°

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