1 / 13

Properties of Parallelograms

Properties of Parallelograms. In this lesson. And the rest of the chapter, you will study special quadrilaterals. A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

pancho
Download Presentation

Properties of Parallelograms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Properties of Parallelograms

  2. In this lesson . . . And the rest of the chapter, you will study special quadrilaterals. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. When you mark diagrams of quadrilaterals, use matching arrowheads to indicate which sides are parallel. For example, in the diagram to the right, PQ║RS and QR║SP. The symbol PQRS is read “parallelogram PQRS.”

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

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

  5. Theorems about parallelograms • 6.4—If a quadrilateral is a parallelogram, then its consecutive anglesare 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° Q R P S

  6. Theorems about parallelograms Q R • 6.5—If a quadrilateral is a parallelogram, then its diagonals bisect each other. QM ≅ SM and PM ≅ RM P S

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

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

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

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

  11. Ex. 2: Using properties of parallelograms R Q 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. b. 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. 70° P S

  12. Ex. 3: Using Algebra with Parallelograms P Q PQRS is a parallelogram. Find the value of x. mS + mR = 180° 3x + 120 = 180 3x = 60 x = 20 Consecutive s of a □ are supplementary. Substitute 3x for mS and 120 for mR. Subtract 120 from each side. Divide each side by 3. 3x° 120° S R

  13. Ex. 1: Using properties of Parallelograms • 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. 5 G F 3 K H J • JK = GK Diagonals of a bisect each other. • JK = 3

More Related