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Tests for Parallelograms

Tests for Parallelograms. Parallelogram Sec : 8.3 Sol: G.8 a,b,c. Proving Parallelograms. Theorem 8.9 : If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

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Tests for Parallelograms

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  1. Tests for Parallelograms Parallelogram Sec: 8.3 Sol: G.8 a,b,c

  2. Proving Parallelograms Theorem 8.9 : If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 8.10 : If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.

  3. Theorem 8.11 : If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Theorem 8.12 : If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

  4. Summary – Tests for Parallelograms • Both pairs of opposite sides are parallel (Definition) • Both pairs of opposite sides are congruent (Thm 8.9) • Both pairs of opposite angles are congruent (Thm 8.10) • Diagonal bisect each other (Thm 8.11) • A pair of opposite sides are both parallel and congruent (thm 8.12)

  5. Find the values of x and y the ensure each quadrilateral is a parallelogram

  6. Example: Solve for x and y. 2y+12 x Y 5x - 28 5y

  7. Suggested assignments Classwork: Workbook pg 94 1-10 and 95 1-6 Homework: Pg 420 1-7, 14-22e Quadrilateral Parallelogram

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