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DRILL

DRILL. 1. Name 6 Different types of Quadrilaterals. 2. Are all Squares considered Rectangles? 3. Are all Parallelograms considered Rectangles? 4. How would you find the third side of a right triangle given two of the sides?. 9.1 Properties of Parallelograms. Geometry Mr. Calise.

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DRILL

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  1. DRILL 1. Name 6 Different types of Quadrilaterals. 2. Are all Squares considered Rectangles? 3. Are all Parallelograms considered Rectangles? 4. How would you find the third side of a right triangle given two of the sides?

  2. 9.1 Properties of Parallelograms Geometry Mr. Calise

  3. Objectives: • Use some properties of parallelograms. • Use properties of parallelograms in real-life situations.

  4. 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.”

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

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

  7. Properties of a Parallelogram 1. Opposite Sides are Congruent. 2. Opposite Angles are Congruent. 3. Consecutive Angles are Supplementary. 4. Diagonals Bisect each other.

  8. Parallel Lines Cut By A Transversal If three or more parallel lines are cut by a transversal and the parts of the transversal are congruent, then the parts of all other transversals are also congruent.

  9. 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

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

  11. 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.

  12. FGHJ is a parallelogram. Find the unknown length. Explain your reasoning. JH JK 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.

  13. 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 • JK = GK Diagonals of a bisect each other. • JK = 3 Substitute 3 for GK b.

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

  15. 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° S

  16. PQRS is a parallelogram. Find the angle measure. mR mQ 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° S P S

  17. 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. Ex. 3: Using Algebra with Parallelograms Q P 120° 3x° S R

  18. Given: ABCD and AEFG are parallelograms. Prove 1 ≅ 3. ABCD is a □. AEFG is a ▭. 1 ≅ 2, 2 ≅ 3 1 ≅ 3 Given Ex. 4: Proving Facts about Parallelograms

  19. Given Opposite s of a ▭ are ≅ Given: ABCD and AEFG are parallelograms. Prove 1 ≅ 3. 1. ABCD is a □. AEFG is a ▭. 2. 1 ≅ 2, 2 ≅ 3 3. 1 ≅ 3 Ex. 4: Proving Facts about Parallelograms

  20. Given 2. Opposite s of a ▭ are ≅ 3. Transitive prop. of congruence. Given: ABCD and AEFG are parallelograms. Prove 1 ≅ 3. 1. ABCD is a □. AEFG is a ▭. 2. 1 ≅ 2, 2 ≅ 3 3. 1 ≅ 3 Ex. 4: Proving Facts about Parallelograms

  21. Given: ABCD is a parallelogram. Prove AB ≅ CD, AD ≅ CB. Proofs

  22. FURNITURE DESIGN. A drafting table is made so that the legs can be joined in different ways to change the slope of the drawing surface. In the arrangement below, the legs AC and BD do not bisect each other. Is ABCD a parallelogram? Ex. 6: Using parallelograms in real life

  23. ANSWER: NO. If ABCD were a parallelogram, then by definition of a parallelogram, AC would bisect BD and BD would bisect AC. They do not, so it cannot be a parallelogram.

  24. Homework • Textbook Page 451 • #’s 1 – 10, 14 – 16

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