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Understanding Quadrilaterals and Their Properties

This resource provides a comprehensive overview of various types of quadrilaterals, including parallelograms, rectangles, rhombuses, squares, kites, and trapezoids. Each section explains special properties, how to prove parallelism using the slope formula, and methods to determine congruence using the distance formula. The guide also includes practical exercises involving solving for unknowns in geometric figures and classifying triangles. Ideal for students looking to enhance their understanding of geometry and develop problem-solving skills.

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Understanding Quadrilaterals and Their Properties

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  1. ANSWER it if you are genius… • A man and his wife have three sons, and every one of the sons has a sister… • How many are there in the family? • A. 6 B. 8 C. 10 D. 12

  2. Warm up • Identify the transformation ∆RST → ∆XYZ. • Is XY congruent to RS? • What is the length of XY?

  3. Math is brought to you by the number … • April 18, 2013 • Day 65 of 90 • 90-65 =

  4. Types of Quadrilaterals(4-sided figures)

  5. Parallelograms A four sided figure with both pairs of opposite sides parallel

  6. Some Special Properties of Parallelograms • Opposite sides are congruent • Diagonals bisect each other • Both pairs of opposite sides are parallel

  7. To Prove Parallel (use slope formula) • Means opposite sides have the SAME SLOPE Sides Congruent (use distance formula) • Means their distances are the same

  8. Solve for x.

  9. Solve for x.

  10. Rectangle A parallelogram with 4 right angles

  11. Some Special Properties of Rectangles • All the properties of a parallelogram • Diagonals are congruent • 4 right angles

  12. To Prove Parallel (use slope formula) • Means opposite sides have the SAME SLOPE 4 Right Angles (use slope formula) • Means consecutive sides have opposite reciprocal slopes Opposite Sides Congruent (use distance formula) • Means opposite sides have the same distance

  13. Rhombus A parallelogram with 4 congruent sides

  14. Some Special Properties of Rhombus • All the properties of a parallelogram • Diagonals are perpendicular • 4 congruent sides

  15. To Prove Parallel (use slope formula) • Means opposite sides have the SAME SLOPE Perpendicular (use slope formula) • Means diagonals have opposite reciprocal slopes Sides Congruent (use distance formula) • Means their distances are the same

  16. Solve for x in this rhombus.

  17. Rhombus.1. VY =2. mZVY Z

  18. Square A parallelogram with 4 congruent sides & 4 right angles

  19. Some Special Properties of Square • All the properties of a parallelogram, rectangle, & rhombus

  20. Solve for x in this square.

  21. Square1. EJ = 2. HF =3. mEJF4. mHGF

  22. Kite A quadrilateral with 2 pairs of consecutive congruent sides, but opposites sides are NOT parallel

  23. Some Special Properties of Kite • Diagonals are perpendicular

  24. To Prove Not Parallel (use slope formula) • All sides have a different slope 2 Pairs of Consecutive Sides Congruent (use distance formula) • Means two pair of sides have the same distance

  25. Trapezoid A quadrilateral with 1 pair of parallel sides called bases

  26. base leg leg base Trapezoids Have only one pair of opposite sides that are parallel.

  27. Isosceles Trapezoid A quadrilateral with 1 pair of parallel sides called bases and non-parallel sides are congruent (legs)

  28. Some Special Properties of Isosceles Trapezoid • Diagonals are congruent

  29. To Prove Bases Parallel (use slope formula) • Means 1 pair of opposite sides have the SAME SLOPE Legs Congruent (use distance formula) • Means their distances are the same Diagonals Congruent (use distance formula) • Means their distances are the same

  30. Classifying Trianglesby Sides • Equilateral – 3 congruent sides • Isosceles – 2 congruent sides • Scalene – No sides congruent

  31. To Prove Congruent (use distance formula) • Means their distances are the same; figure out how many sides of the triangle have the same distance

  32. Classwork Find the Missing Point Worksheet

  33. Homework Quadrilaterals and Parallelograms Homework Worksheet

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