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Geometry 6.2 Parallelograms

Geometry 6.2 Parallelograms. -A parallelogram is a quadrilateral with both pairs of opposite sides parallel. -The symbol PQRS is read “parallelogram PQRS.”. If a quadrilateral is a parallelogram, then its opposite sides are congruent. Theorem 6.3. Q. R. P. S.

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Geometry 6.2 Parallelograms

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  1. Geometry6.2 Parallelograms

  2. -A parallelogram is a quadrilateral with both pairs of opposite sides parallel. -The symbol PQRS is read “parallelogram PQRS.”

  3. If a quadrilateral is a parallelogram, then its opposite sides are congruent. Theorem 6.3 Q R P S

  4. If a quadrilateral is a parallelogram, then its opposite angles are congruent. Theorem 6.4 Q R P S

  5. If a quadrilateral is a parallelogram, then its consecutive angles are supplementary (add up to 180°). mP +mQ = 180°, mQ +mR = 180° Theorem 6.5 Q R P S

  6. Theorem 6.6 • -If one angle of a parallelogram is right, then all 4 angles are right.

  7. If a quadrilateral is a parallelogram, then its diagonals bisect each other. Theorem 6.7 Q R P S

  8. FGHJ is a parallelogram. Find the unknown length. Explain your reasoning. JH JK Ex. 1 5 G F 3 K H J b.

  9. PQRS is a parallelogram. Find the angle measure. mR mQ Ex. 2 Q R 70° P S

  10. PQRS is a parallelogram. Find the value of x. Ex. 3: Using Algebra with Parallelograms P Q 3x° 120° S R

  11. Given: ABCD and AEFG are parallelograms. Prove 1 ≅ 3. Ex. 4

  12. Example 5 • What are the coordinates of the intersection of the diagonals of parallelogram MNPR with vertices M(-3,0), N(-1, 3), P(5, 4), R(3,1)?

  13. Homework • Page 403: (2-21, 31-36, 50-57) all

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