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Parallelograms & Tests for Parallelograms

Parallelograms & Tests for Parallelograms. Notes 22 – Sections 6.2 & 6.3. Essential Learnings. Students will understand and be able to recognize and apply properties of parallelograms.

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Parallelograms & Tests for Parallelograms

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  1. Parallelograms &Tests for Parallelograms Notes 22 – Sections 6.2 & 6.3

  2. Essential Learnings • Students will understand and be able to recognize and apply properties of parallelograms. • Students will understand and be able to recognize the conditions that ensure a quadrilateral is a parallelogram.

  3. Properties of Parallelograms • If a quadrilateral is a parallelogram, then its opposite sides are congruent.

  4. Properties of Parallelograms • If a quadrilateral is a parallelogram, then its opposite angles are congruent.

  5. Properties of Parallelograms • If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. mA + mB = 180  mB + mC = 180  mC + mD = 180  mD + mA = 180  B A C D

  6. Properties of Parallelograms • If a parallelogram has one right angle, then it has four right angles.

  7. Example 1 In parallelogram ABCD, suppose m∠B = 32, CD = 80 inches, and BC = 15 inches. Find each measure. AD = m∠C = m∠D = A B D C

  8. Diagonals of Parallelograms • If a quadrilateral is a parallelogram, then its diagonals bisect each other.

  9. Diagonals of Parallelograms • If a quadrilateral is a parallelogram, then each diagonal separates the parallelogram into two congruent triangles.

  10. Example 2 If JKLM is a parallelogram, find the value of the indicated variable. x = y= z = 2zº 4x J K 7y+3 8y 40º 18º L 18 M

  11. Conditions for Parallelograms • If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. A B ABDC ADBC then ABCD is a parallelogram. D C

  12. Conditions for Parallelograms • If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. W X mWmY mZmX then WXYZ is a paralellogram. Z Y

  13. Conditions for Parallelograms • If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

  14. Conditions for Parallelograms • If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.

  15. Example 3 Determine whether the quadrilateral is a parallelogram. Justify your answer. 100º 14 14 80º

  16. Example 4 Determine whether the quadrilateral is a parallelogram. Justify your answer. 71º 70º

  17. Example 5 Find x and y so that the quadrilateral is a parallelogram. 4x-1 3(y+1) 4y-2 3(x+2)

  18. Example 6 Find x and y so that the quadrilateral is a parallelogram. -2x+6 -4y-2 x+12 y+23

  19. Assignment p. 403: 9 - 12, 15 - 20, 31 - 36 p. 414: 9 - 14, 18 – 23

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