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Lesson 8-3

Tests for Parallelograms. Lesson 8-3. 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.

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Lesson 8-3

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  1. Tests for Parallelograms Lesson 8-3

  2. 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 .

  3. 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

  4. 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 .

  5. Examples …… Example 1: Find the value of x and y that ensures the quadrilateral is a parallelogram. y+2 6x 4x+8 2y Find the value of x and y that ensure the quadrilateral is a parallelogram. Example 2: (2x + 8)° 120° 5y°

  6. Examples …… Example 3: Find the value of x and y that ensures the quadrilateral is a parallelogram. 5x + 12 3y + 6 5y-6 8x Find the value of x and y that ensure the quadrilateral is a parallelogram. Example 4: y+7 4x 2y 5x - 4

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