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Quadrilaterals

Materials: Straightedge 2 sheets of Patty Paper. Quadrilaterals. To recognize and define parallelograms, rectangles, squares, rhombus, and trapezoids Use properties of above shapes to solve problems. Parallelogram Properties.

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Quadrilaterals

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  1. Materials: Straightedge 2 sheets of Patty Paper Quadrilaterals To recognize and define parallelograms, rectangles, squares, rhombus, and trapezoids Use properties of above shapes to solve problems

  2. Parallelogram Properties • Use a ruler to draw two sets of intersecting parallel lines on your patty paper. Label the parallelogram ABCD. • Place a second patty paper over the first and trace ABCD. Label the second parallelogram PQRS.

  3. Continue • Move the second patty paper over the first and compare side RS to side AB. How do the lengths of the opposite sides compare? • Rotate and move the second patty paper over the first to compare opposite angles R and A or angles S and B. How do the opposite angles compare? • Rotate the second patty paper around the first to compare<S and <A. What is their relationship? What can be drawn?

  4. Quadrilaterals • Essential Question: How to use the properties of quadrilaterals to find the missing measures?

  5. Quadrilaterals • Four-sided polygons • Angles have the sum of 360 degrees

  6. Polygon • Closed figure • Formed by segments • Essentials: • Nonessentials:

  7. Parallelogram • Two sets of parallel sides • Opposite sides are congruent • Opposite angles are congruent • Consecutive angles are supplementary • Diagonals bisect each other • It’s a quadrilateral

  8. Rectangle • Two sets of parallel sides • Opposite sides are congruent • All angles are congruent • Diagonals are congruent and bisect each other • It’s a parallelogram

  9. Rhombus • Two sets of parallel sides • All sides are congruent • Opposite angles are congruent • Consecutive angles are supplementary • Diagonals are perpendicular, bisect each other, and bisect the angles • It’s a parallelogram

  10. Square • Two sets of parallel sides • All sides are congruent • All angles are congruent • Diagonals are congruent, perpendicular, bisect each other, and bisect the angles • It’s a parallelogram, rectangle, and rhombus

  11. Trapezoid • Exactly one pair of parallel sides • Parallel sides are bases • Nonparallel sides are legs • If legs are congruent, then its an isosceles trapezoid • Diagonals are congruent • Median is a segment that joins the midpoints of its legs • M= ½ (b1 + b2) • It’s a quadrilateral.

  12. Complete •  8.2 Parallelograms •  8.4 Rectangles, Rhombi, and Squares •  (back) Quadrilaterals

  13. MondayWarm-Up: find the missing measures • Parallelogram • Square 3 12 15 61 30 27 18

  14. Practice • Complete •  8.2 Parallelograms •  8.4 Rectangles, Rhombi, and Squares •  (back) Quadrilaterals • USE: • Quadrilateral Info Sheet YOU MAY WORK WITH A PARTNER Quiz on Tuesday

  15. Polygon Hierarchy Polygons Quadrilaterals Parallelograms Trapezoid Rectangles Rhombus Square

  16. Polygon Hierarchy • ~ Some classes of polygons are quadrilaterals, parallelograms, rectangles, trapezoids, rhombi, and squares. These classes are arranged in the hierarchy on next slide. Directions: • Copy hierarchy. • Explain in details (complete sentences) why the shapes are arranged as so. Use your yellow sheet, textbook, Geometry to Go, and/or internet as a reference. • Be creative. You may write an explanation under each box, use poster board, etc. • Find a real world picture for all seven shapes. •  Due Date: Tuesday

  17. Polygon Hierarchy Polygons Quadrilaterals Parallelograms Trapezoid Rectangles Rhombus Square

  18. TuesdayWarm-Up: find the missing measures • Rectangle • X = • Square • X = (2x + 8)º (2x + 16) (4x + 6) 67

  19. Practice Questions

  20. Define quadrilateral. • Answer: • Four sided figure. • Angle sum = 360ºº

  21. Explain why a square is a rectangle, and why a rectangle is not considered as a square. • Answer: • A square always have 4 congruent sides where as a rectangles sometime have 4 congruent sides.

  22. Properties of an isosceles trapezoid • Answer: • Congruent Legs • Bases are parallel • Base angles are congruent • Diagonals are congruent

  23. Parallelogram, rectangle, rhombus, or square? • All angles are congruent. • Answer: • Rectangle and square

  24. Parallelogram, rectangle, rhombus, or square? • All sides are congruent. • Answer: • Rhombus and square

  25. Parallelogram, rectangle, rhombus, or square? • Diagonals are perpendicular. • Answer: • Rhombus and square

  26. Parallelogram, rectangle, rhombus, or square? • All sides and angles are congruent. • Answer: • square

  27. QUIZ TIME • ABSOLUTELY NO TALKING • Work on your Polygon Hierarchy following quiz.

  28. MondayWarm-Up: find the missing measures • Parallelogram • Rhombus 3 14 15 61 23 48 27 16

  29. Trapezoid • Draw an isosceles trapezoid ABCD • Label the bases and legs • What do know about the legs? • Draw the diagonals • What do know about the diagonals? • Draw an isosceles trapezoid WXYZ • Draw a median and label legs • What is the formula to find the median B A D C W X Z Y

  30. Isosceles Trapezoid • If LK = 30, HJ = 42, Find RS. • If RS = 17, HJ = 14, Find LK. • H • If RS = x + 5, (HJ + LK) = 4x + 6, Find RS. K L S R J

  31. Isosceles Trapezoid 110 10 24 36

  32. Practice: Quadrilaterals/Trapezoids • Complete 8.1 and 8.5 • Complete QuadPrac • Quiz: Tuesday • Project DUE Tuesday • Test: Monday

  33. ACTIVITY 1 Polygon Hierarchy All due TOMORROW! • Explain why the shapes are arranged as is and attach a real world picture to each. • Critical Thinking • Know the properties of each quadrilateral • Find the missing measures • Solve for x. Polygons ACTIVITY 2 Quadrilaterals Parallelograms Trapezoid QuadPrac Rhombus Rectangles Square

  34. Tuesday Warm-Up • 1. B A C D • Given ABCD, m< A = 3x + 4 and m< C = 5x – 28, find m< B. • 2. Two adjacent angles of a parallelogram have measures (3x – 2) and (4x + 7). Find x. • 3. X Y M N W Z WXYZ is a trapezoid. M is the midpoint of XW and N is the midpoint of YZ. If WZ = 25 and MN = 18, find XY. If <Y is 123°, find <W. • 4. Rectangle 36º 10

  35. ACTIVITY Polygon Hierarchy ACTIVITY • Project is due TODAY! • Explain why the shapes are arranged as is and attach a real world picture to each. • NO talking during quiz • Do your BEST! Quiz: Trapezoid Polygons Quadrilaterals Parallelograms Trapezoid • Tuesday Agenda • Turn in Polygon Hierarchy • √ QuadPrac • Take Quiz: Trapezoids • Complete Study Guide (Test Wednesday) Rhombus Rectangles Square

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