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6.1 Properties of Parallelograms

6.1 Properties of Parallelograms. Objectives:. Use some properties of parallelograms. In this lesson. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. In the diagram to the right, PQ ║RS and QR║SP. The symbol PQRS is read “parallelogram PQRS.”.

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6.1 Properties of Parallelograms

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  1. 6.1 Properties of Parallelograms

  2. Objectives: • Use some properties of parallelograms.

  3. In this lesson . . . A parallelogram is a quadrilateral with both pairs of opposite sides parallel. In the diagram to the right, PQ║RS and QR║SP. The symbol PQRS is read “parallelogram PQRS.”

  4. f a quadrilateral is a parallelogram, then its opposite sides are congruent. ►PQ≅RS and SP≅QR Theorems about parallelograms Q R P S

  5. If a quadrilateral is a parallelogram, then its opposite angles are congruent. P ≅ R and Q ≅ S Theorems about parallelograms Q R P S

  6. 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°, mR + mS = 180°, mS + mP = 180° Theorems about parallelograms Q R P S

  7. If a quadrilateral is a parallelogram, then its diagonals bisect each other. QM ≅ SM and PM ≅ RM Theorems about parallelograms Q R P S

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

  9. FGHJ is a parallelogram. Find the unknown length. Explain your reasoning. JH JK SOLUTION: a. JH = FG Opposite sides of a are ≅. JH = 5 Substitute 5 for FG. Ex. 1: Using properties of Parallelograms 5 G F 3 K H J b.

  10. FGHJ is a parallelogram. Find the unknown length. Explain your reasoning. JH JK SOLUTION: a. JH = FG Opposite sides of a are ≅. JH = 5 Substitute 5 for FG. Ex. 1: Using properties of Parallelograms 5 G F 3 K H J b. • JK = GK Diagonals of a bisect each other. • JK = 3 Substitute 3 for GK

  11. PQRS is a parallelogram. Find the angle measure. mR mQ Ex. 2: Using properties of parallelograms Q R 70° P S

  12. PQRS is a parallelogram. Find the angle measure. mR mQ a. mR = mP Opposite angles of a are ≅. mR = 70° Substitute 70° for mP. Ex. 2: Using properties of parallelograms Q R 70° P S

  13. PQRS is a parallelogram. Find the angle measure. mR mQ a. mR = mP Opposite angles of a are ≅. mR = 70° mQ + mP = 180° Consecutive s of a are supplementary. mQ + 70° = 180° Substitute 70° for mP. mQ = 110° Subtract 70° from each side. Ex. 2: Using properties of parallelograms Q R 70° P S

  14. PQRS is a parallelogram. Find the value of x. mS + mR = 180° 3x + 120 = 180 3x = 60 x = 20 Ex. 3: Using Algebra with Parallelograms P Q 3x° 120° S R

  15. Lets Practice 125 45 5x- 3 = 2x +9 3x- 3 = 9 3x= 12 X = 4 AB = 5*4 – 3 AB = 17 180-135 = 45 180-50 = 130

  16. Lets Practice 2x – 10 + 3x = 180 5x – 10 = 180 5x = 190 X = 38 DAB = 2 * 38 – 10 DAB = 66

  17. Lets Practice 3x – 12 = x + 40 2x – 12 = 40 2x = 52 X = 26 BAD = 3 * 26 - 12 BAD = 66

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