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Exploring Quadrilaterals and Properties with Patty Paper

Use a straightedge and patty paper to recognize and define different quadrilaterals such as parallelograms, rectangles, squares, rhombi, and trapezoids. Apply properties of these shapes to solve problems and find missing measures in a fun and engaging way.

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Exploring Quadrilaterals and Properties with Patty Paper

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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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