Quadrilaterals grade 7

basic properties of quadrilaterals

1. REVIEW What is a triangle? Triangle is a polygon with 3 angles and 3 straight sides.

2. REVIEW What are angles as classified according to the number of congruent sides? - Isosceles Triangle - Scalene Triangle - Equilateral Triangle

3. REVIEW What are angles as classified according to the measures of their angles? Acute Triangle Right Triangle Obtuse Triangle Equiangular Triangle

4. Quadrilateral What is a quadrilateral? Quadrilateral is a polygon with 4 sides and 4 angles

5. QUADRILATERAL N A M E 4 sides 4 vertices 4 angles         N A M E        

6. Quadrilateral Quadrilaterals are denoted by its vertices , written consecutively in clockwise or counterclockwise direction. In the figure, the quadrilateral can be denoted by NAME AMEN MENA ENAM N A M E NEMA EMAN MANE ANEM Counter Clockwise Clockwise

7. QUADRILATERAL N A M E On the same figure, we have         and and - 2 pairs of opposite ANGLES namely - 2 pairs of opposite SIDES namely         and and - 2 DIAGONALS namely     and

8. QUADRILATERAL N A M E - 4 pairs of CONSECUTIVE ANGLES - 4 pairs of CONSECUTIVE SIDES     and     and     and     and     and     and     and     and

9. Using the quadrilateral, identify: Two pairs of opposite angles 2. Two pairs of opposite sides 3. One pair of diagonals 4. Two pairs of opposite vertices 5. Four pairs of consecutive sides 6. Four pairs of consecutive angles S E A M

10. Sum of the angles in a Quadrilateral 180° 180° 180° + 180° = 360°

11. Quadrilateral The sum of the angles of a quadrilateral measures 360 95 95 85 85

12. Sum of the angles

13. Sum of the angles

14. Find the angles marked with letters. (Note: Figures are not drawn to scales.) 55

15. Find the angles marked with letters. (Note: Figures are not drawn to scales.) 116

16. Find the angles marked with letters. (Note: Figures are not drawn to scales.) 67

17. Find the angles marked with letters. (Note: Figures are not drawn to scales.) 169

18. Find the angles marked with letters. (Note: Figures are not drawn to scales.) 144° 36° 83°

19. Find the angles marked with letters. (Note: Figures are not drawn to scales.) 138° 42° 42° 138°

20. Classification of Quadrilateral Trapezoid A trapezoid is a quadrilateral with exactly a pair of parallel sides This trapezoid has one pair of parallel sides. Can you identify which two sides are parallel? Do trapezoids have to have sides that are congruent? L M N K

21. Quadrilateral L M N K base base Base angles leg leg Trapezoid

22. Trapezoid B C D A Isosceles Trapezoid If the legs of a trapezoid are congruent

23. Quadrilateral E C S D TRAPEZIUM If the quadrilateral has no parallel sides

24. Quadrilateral D C E F Parallelogram It is a quadrilateral with two pairs of congruent and parallel sides This parallelogram has two pairs of parallel sides. Can you draw a parallelogram that looks different than this one?

25. Properties of a Parallelogram 1. Opposite sides are congruent . E D C F

26. 2. Opposite angles are congruent . Properties of a Parallelogram D C E F

27. 3. Consecutive angles are supplementary Properties of a Parallelogram D C E F 105° 75° 105° 75° 105° + 75° = 180° 75° + 105° = 180° 75° + 105° = 180° 105° + 75° = 180°

28. 4. The diagonals of a parallelogram bisect each other. Properties of a Parallelogram D C E F G

29. 5. Each diagonal of a parallelogram separates it into two congruent triangles Properties of a Parallelogram D C E F D C E F

30. Properties of a Parallelogram 1. Opposite sides are congruent . 2. Opposite angles are congruent . 3. Consecutive angles are supplementary 4. The diagonals of a parallelogram bisect each other. 5. Each diagonal of a parallelogram separates it into two congruent triangles E D C F

31. Using the parallelogram, identify: Two pairs of congruent opposite sides Two pairs of opposite congruent angles Four pairs of consecutive angles that are supplementary Two pairs of triangle that are congruent L I M E N

32. Seat Work

33. A. Using the parallelogram, identify: Two pairs of congruent opposite sides Two pairs of opposite congruent angles One pair of diagonals Two pairs of triangle that are congruent Four pairs of consecutive angles that are supplementary A N D L E

34. B. Find the angles marked with letters. (Note: Figures are not drawn to scales.) 1. 2.

35. Find the angles marked with letters. (Note: Figures are not drawn to scales.) 3. 4.

36. Find the angles marked with letters. (Note: Figures are not drawn to scales.) 5. 6.

37. Special Parallelograms They are classified by their sides and their angles Rectangle Rhombus Square

38. Properties of a Parallelogram 1. Opposite sides are congruent . 2. Opposite angles are congruent . 3. Consecutive angles are supplementary 4. The diagonals of a parallelogram bisect each other. 5. Each diagonal of a parallelogram separates it into two congruent triangles E D C F

39. Special Parallelograms They are classified by their sides and their angles G H I F A rectangle is a parallelogram with four angles RECTANGLE This rectangle has four right angles and two pairs of parallel sides that are congruent. If all four sides were equal, would this shape still be a rectangle?

40. Special Properties of Rectangle A diagonal of a rectangle divides the rectangle into two congruent right triangles A D C B

41. Special Properties of Rectangle Diagonals of a rectangle are congruent. A D C B

42. Special Parallelograms A rhombus is a parallelogram with four congruent side RHOMBUS N O P M This rhombus has four congruent sides and two pairs of parallel sides. Can a square be a rhombus?

43. Special Properties of Rhombus Diagonals of a rhombus are perpendicular. S T N E

44. Special Parallelograms - A square is a parallelogram with four congruent sides and four congruent angles SQUARE R Q T S - A square is also a rhombus with four congruent angles This square has four right angles and all four sides are congruent (the same length). How many pairs or sets of parallel sides do you see?

45. Special Properties of Square A diagonal of a square divides the square into two congruent isosceles right triangles F E N I

46. F E N I Special Properties of Square Diagonals of a square are both congruent and perpendicular.

47. List each special quadrilateral that satisfies the given set of conditions It has four sides. 2. It has two sets of parallel sides. 3. It has four congruent sides 4. It has four right angles 5. It has exactly one set of parallel sides

48. Quadrilateral Parallelogram Rhombus Rectangle Square Trapezoid Isosceles Trapezoid Trapezium The sum of the angles measures 360

49. Classify each statement as True or False. Every rectangle is quadrilateral. Every rectangle is a parallelogram Every trapezoid is a parallelogram Every square is a rectangle Every parallelogram is a square Every trapezoid is a quadrilateral Every square is a rhombus Every rhombus is a parallelogram A square is both a rectangle and a rhombus A rectangle is a quadrilateral and a parallelogram.

50. Classify each statement as True or False. Every rectangle is quadrilateral. Every rectangle is a parallelogram Every trapezoid is a parallelogram Every square is a rectangle Every parallelogram is a square Every trapezoid is a quadrilateral Every square is a rhombus Every rhombus is a parallelogram A square is both a rectangle and a rhombus A rectangle is a quadrilateral and a parallelogram. TRUE TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE