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Understanding Linear Functions and Parallelograms in Geometry

Learn about identifying linear functions with ordered pairs and properties of parallelograms with this comprehensive guide. Practice problems included for better understanding.

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Understanding Linear Functions and Parallelograms in Geometry

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  1. Bell Ringer 10/18/2011 Which set of ordered pairs could be ordered pairs of a linear function? a.{(0,0),(1,1),(2,8),(3,27)} b.{(0,0),(1,1),(2,4),(3,9)} c.{(0,0),(1,1),(2,2),(3,3)} d.{(0,0),(1,1),(2,-1),(3, -4)} According to a pedometer, it was 3600 steps around a square walking path. What would be the area of the land bordered by the walking path in square yards if the average step is about 2.25 feet? a. 405,000 yd² b. 450,000 yd² c. 455,625 yd² d. 562,500 yd²

  2. 8.2 Parallelograms • How can we recognize and apply properties of the sides, angles, and diagonals of parallelograms?

  3. Parallelogram • A parallelogram is a quadrilateral with both pairs of opposite sides parallel A B D C Symbols: ABCD ; AB||DC and AD||BC

  4. Properties of Parallelograms A B C D G H K J

  5. More Properties of Parallelograms • The diagonals of a parallelogram bisect each other • RQ=QT and SQ=QU • Each diagonal of a parallelogram separates the parallelogram into two congruent triangles. • ∆RUT≅∆TSR • ∆SRU≅∆UTS R S Q U T

  6. Also… • If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.

  7. 8.2 & 8.3 Practice Problems: • 8.2 #’s 17, 23, 37 • 8.3 #’s 13, 19, 25

  8. HW 8.2 & 8.3 • 8.2 #’s 17-39odd • 8.3 #’s 13-33odd

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