1. Journal 6: Polygons
Delia Coloma 9-5

2. What is a polygon?
Sides:
3. Triangle
4. Quadrilateral
5. Pentagon
6. Hexagon
7. Heptagon
8. Octagon
9. Nonagon
10. Decagon
12. Dodecagon
A Polygon is a 2-dimensional shape made up of straight lines, and closed. This means that all the lines need to connect .

3. Found example:

4. Parts of a polygon:
Diagonal
Vertex
side

5. Real life examples:

6. Concave vs. Convex Convex: Concave: It is when a polygon has
all vertices pointing
outwards.
Example 1)
Example 2)
Example 3)
Concave:
It is when any figure has
1 or more vertices
pointing inwards.
Example 1)
Example 2)
Example 3)

7. Real life example:
Concave:
Convex:

8. Equilateral vs. equiangular
It is when all of the sides
are congruent.
Equiangular:
It is when all of the
angles are congruent.
1 m
14 cm
2 in

9. Real Life example:
Equiangular:
Equilateral:

10. Then divide by the number of sides.
 Interior angles theorem for polygons:
If it is a regular polygon: To find each interior angle, you need to use this formula:
N-2 x 180
Then divide by the number of sides.

11. Examples: Hexagon 6-2=4 4x180= 720 720/6=120 quadrilateral 4-2=2
Heptagon
5-2=3
3x180=540
540/5=108
4-2=2
2x180=360
360/4=90

12. Real life example:
6-2=4
4x180= 720
720/6=120

13. Theorems of Parallelograms:
Opposite sides are congruent
Definition of parallelogram: quadrilateral that has opposite sides parallel to each other.
Opposite angles are congruent
Diagonals bisect each other
Consecutive angles are supplementary
It has one set of congruent and parallel sides.

14. Converse of theorems of parallelograms:
If it is a parallelogram then opposite sides are congruent
quadrilateral that has opposite sides parallel to each other is a parallelogram
If their opposite angles are congruent, then it is a parallelogram
The diagonals will bisect each other if it is a parallelogram.
If the consecutive angles are supplementary then it is a parallelogram
If it has one set of congruent and parallel sides, then it is a parallelogram.

15. How to prove that quadrilateral is a parallelogram…b c d 1 2 3 4
Given: AB is congruent to CD, BC is cong. To DA
Prove: ABCD is a parallelogram.
statement
reason
Ab is cong to cd, bc is congr to da
given
Bd is cong to bd
Reflexive property
Triangle dab is cong to dcb
sss
<1 is cong to <3, <4 is cong to <2
cpct
Ab || to cd, bc is || to da
Abcd is a parallelogram
Alternate int. Angles tm
Def of parallelogram

16. Rhombus, squares and rectangles:

17. Rectangles: It is any parallelogram with 4 right angles.
1. The diagonals bisect each other, so they are congruent.
Example 2)
Example 1)
Example 3)

18. Real life example:

19. Rectangle theorems:

20. Theorem 6-5-1:
If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle.

21. Theorem 6-5-2:
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

22. Rhombus: A parallelogram with 4 congruent sides.
1. Diagonals are perpendicular.
Example 1)
Example 3)
Example 2)

23. Real life example:

24. Rhombus theorems:

25. Theorem 6-5-3:
If one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.

26. Theorem 6-5-4:
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

27. Theorem 6-5-5:
If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.

28. Squares: A parallelogram that is both a rectangle and a rhombus.
1) Has parallelogram characteristics.

29. “Cartoon life example:”

30. Trapezoids: A quadrilateral with one pair of parallel sides. Base 2
leg
Properties of an isosceles trapezoid:
Diagonals are congruent
Base angles (both sets) are congruent.
Opposite angles are supplementary.
Isosceles trapezoid: a trapezoid with a pair of congruent legs.

31. Examples:

32. Real life example:

33. Trapezoidal theorems:

34. Theorem 6-6-3
If a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent.

35. Theorem 6-6-4
If a trapezoid has one pair of congruent base angles, then the trapezoid isosceles.

36. Theorem 6-6-5:
A Trapezoid is isosceles if and only if its diagonals are congruent.

37. Trapezoid midsegment theorem:
The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the length of the bases.

38. Kite: Has two pairs of congruent adjacent sides.
Diagonals are perpendicular
One pair of congruent angles (the ones formed by non-congruent sides)
One of the diagonals bisects the other.

39. Examples:

40. Real life example:

41. Kite theorems:

42. Theorem 6-6-1:
If a quadrilateral is a kite, then its diagonals are perpendicular.

43. Theorem 6-6-2:
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

44. THE END (: