basic properties of quadrilaterals

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

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

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

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

6. QUADRILATERAL
N
A M
E
4 sides
4 vertices
4 angles
𝑁𝐸 𝐸𝑀 𝑀𝐴 𝐴𝑁
N A M E
∠𝑁 ∠𝐴 ∠𝑀 ∠𝐸

7. 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

8. QUADRILATERAL
N
A M
E
On the same figure, we have
𝑁𝐴 𝐸𝑀 𝑁𝐸 𝐴𝑀and and
- 2 pairs of opposite ANGLES namely
- 2 pairs of opposite SIDES namely
∠𝑁 ∠𝑀 ∠𝐴 ∠𝐸and and
- 2 DIAGONALS namely
𝑁𝑀 𝐴𝐸and

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

10. Using the quadrilateral, identify:
1. 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

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

12. Quadrilateral
The sum of the angles of a
quadrilateral measures 3600
95
95
85
85

13. Sum of the angles

14. Sum of the angles

15. Find the angles marked with letters.
(Note: Figures are not drawn to scales.)
550

16. Find the angles marked with letters.
(Note: Figures are not drawn to scales.)
1160

17. Find the angles marked with letters.
(Note: Figures are not drawn to scales.)
670

18. Find the angles marked with letters.
(Note: Figures are not drawn to scales.)
169 0

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

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

21. Classification of Quadrilateral
Trapezoid
A trapezoid is a quadrilateral with
exactly a pair of parallel sides
Thistrapezoid hasonepair ofparallel
sides. Can you identifywhichtwo
sides are parallel? Do trapezoids have
to havesides that are congruent?
L M
NK

22. Quadrilateral
L M
NK
base
base
Base angles
leg leg
Trapezoid

23. Trapezoid
B C
DA
Isosceles Trapezoid
If the legs of a trapezoid are congruent

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

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

26. Properties of a Parallelogram
1. Opposite sides are congruent .
ED
C F

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

28. 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°

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

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

31. 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
ED
C F

32. Using the parallelogram, identify:
1. Two pairs of congruent
opposite sides
2. Two pairs of opposite
congruent angles
3. Four pairs of consecutive
angles that are supplementary
4. Two pairs of triangle that are
congruent
L I
ME
N

33. Seat Work

34. A. Using the parallelogram,
identify:
1. Two pairs of congruent
opposite sides
2. Two pairs of opposite
congruent angles
3. One pair of diagonals
4. Two pairs of triangle that are
congruent
5. Four pairs of consecutive
angles that are supplementary
N
L

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

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

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

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

39. 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
ED
C F

40. Special Parallelograms
They are classified by their sides and their angles
G H
IF
A rectangle is a parallelogram with four angles
RECTANGLE
Thisrectanglehas fourright angles and two
pairs ofparallel sides that arecongruent.If
all foursides were equal, would this shape
still be a rectangle?

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

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

43. Special Parallelograms
A rhombus is a parallelogram with four congruent side
RHOMBUS
N
O
P
M
Thisrhombushasfour
congruentsides and two pairs of
parallel sides. Can a squarebe a
rhombus?

44. Special Properties of Rhombus
Diagonals of a rhombus are perpendicular.
S T
NE

45. 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
Thissquarehas fourright angles and all
foursides arecongruent(thesame length).
How many pairs or sets ofparallel sides do
you see?

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

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

48. List each special quadrilateral that satisfies the
given set of conditions
1.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

49. Quadrilateral
Parallelogram
RhombusRectangle
Square
Trapezoid
Isosceles
Trapezoid
Trapezium
The sum of the
angles measures
3600

50. Classify each statement as True or False.
1. Every rectangle is quadrilateral.
2. Every rectangle is a parallelogram
3. Every trapezoid is a parallelogram
4. Every square is a rectangle
5. Every parallelogram is a square
6. Every trapezoid is a quadrilateral
7. Every square is a rhombus
8. Every rhombus is a parallelogram
9. A square is both a rectangle and a rhombus
10.A rectangle is a quadrilateral and a parallelogram.

51. Classify each statement as True or False.
1. Every rectangle is quadrilateral.
2. Every rectangle is a parallelogram
3. Every trapezoid is a parallelogram
4. Every square is a rectangle
5. Every parallelogram is a square
6. Every trapezoid is a quadrilateral
7. Every square is a rhombus
8. Every rhombus is a parallelogram
9. A square is both a rectangle and a rhombus
10.A rectangle is a quadrilateral and a parallelogram.
TRUE
TRUE
FALSE
TRUE
FALSE
TRUE
TRUE
TRUE
TRUE
TRUE