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Properties of Paralleograms

Properties of Paralleograms. Unit 3: Lesson 4. In this lesson. 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.

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Properties of Paralleograms

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  1. Properties of Paralleograms Unit 3: Lesson 4

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

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

  5. 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° Theorems about parallelograms Q R P S

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

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

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

  9. 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 Supp. Substitute 3x for mS and 120 for mR. Subtract 120 from each side. Divide each side by 3. Ex. 3: Using Algebra with Parallelograms P Q 3x° 120° S R

  10. EXAMPLES: Find the value of each variable in the parallelogram 1.) 16 2.) 2a + 1 7 2x 2b - 3 10 21 Y + 2 4.) 52o 3.) 4(p+3) 4m 135o

  11. More Examples: Find the indicated measure in PQRS P Q 2n 3m 12 – n 2xo 15 5(x+1)o S R 1. PR 2. ST 3. m<SRQ 4. m<PQR

  12. Classwork/Homework Page 306 #’s 1-27 ALL

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