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Parallelograms

Parallelograms. Unit 9, Lesson 2 & 3. What is a parallelogram?. By definition, a parallelogram is a quadrilateral with both pairs of opposite sides parallel. Parallelograms have: 2 sets of parallel sides 2 sets of congruent sides opposite angles congruent consecutive angles supplementary

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Parallelograms

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  1. Parallelograms Unit 9, Lesson 2 & 3

  2. What is a parallelogram? • By definition, a parallelogram is a quadrilateral with both pairs of opposite sides parallel. • Parallelograms have: • 2 sets of parallel sides • 2 sets of congruent sides • opposite angles congruent • consecutive angles supplementary • diagonals bisect each other • diagonals form 2 congruent triangles

  3. Example #1 • Complete each statement about parallelogram QRST. • Justify your answer. • ∠TSR is supplementary to _____.

  4. Example #2 • Use parallelogram JKLM to find each measure or value. • m∠MJK = _____ • m∠JML = _____ • m∠JKL = _____ • m∠KJL = _____ E. a = _____ F. b = _____

  5. Example #3 • Parallelogram GHJK has vertices G(-3, 4), H(1, 1), and J(3, -5). Which are possible coordinates for vertex K? • (-1, 1) • (-2, 0) • (-1, -2) • (-2, -1)

  6. The following quadrilaterals are parallelograms. Solve for x and y. 4. 5. 6. x- 4 (y – 4) (3x + 3) 3y - 8 (x + 27) 2x - 12 3x - 6 3x – 16 3y + 2 x + 18

  7. B A C E D Given:Parallelogram ACDE; Prove: Parallelogram ACDE Given Given Opposite sides of a parallelogram are congruent. Transitive property If two sides of a triangle are congruent, then the angles opposite them are also congruent.

  8. A C B E D Given: Parallelogram ACDE; Prove:∆BDCis isosceles Parallelogram ACDE Given Given Opposite angles of a parallelogram are congruent. Transitive property ∆BDC is isosceles If 2 angles of a triangle are congruent, then the sides opposite them are also congruent. Definition of isosceles triangle

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