1. Journal 6
By: Mariana Botran

2. Polygons
A Polygon is a closed plane figure with three or more straight sides.
examples:
The siluette of that house is a polygon because it is a closed figure with no curved lines.

3. The parts of a polygon are: -sides: each segments
-vertices: are the common endpoints of two points
-diagonals: segment that connects any two nonconsecutive vertices.
vertex
side
vertex
diagonal
diagonal
diagonal
side
side
vertex

4. A convex polygon is a polygon in which all vertices are pointing out.
Examples:

5. A concave polygon is a figure that has one or more vertices pointing in.
Examples:

6. Equilateral is when all the sides of the polyogon are congruuent.

7. Equiangular is when all the angles of a polygon are congruent.

8. Interior Angle Theorem for Polygons:
The number of sides minus two and then multiplied times 180 will tell you the sum of the interior angles.
12 – 2 = 10
10 x 180 = 1800
Sum of the interior angles = 1800°
5 – 2 = 3
3 x 180 = 540
Sum of the interior angles = 540 °
examples:
3 – 2 = 1
1 x 180 = 180
Sum of the interior angles = 180°
1800°
540°
180°

9. 4 theorems of parallelograms and its converse:
Theorem 6-2-1: If a quadrilateral is a parallelogram,then its opposite sides are congruent
Converse: If a quadrilateral has its opposite sides that are congruent, then it is a parallelogram.

10. Theorem 6-2-2: If a quadrilateral is a parallelogram,then its opposite angles are congruent.
Converse: If a quadrilateral has opposite angles that are congruent, then it is a parallelogram

11. Theorem 6-2-3: If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
Converse: If a quadrilateral has consecutive angles that are supplementary, then it is a parallelogram. 80
100

12. Theorem 6-2-4: If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Converse: If a quadrilateral has diagonals that bisect eachother, then it is a parallelogram.

13. How to prove that a quadrilateral is a parallelogram.
To know that a quadrilateral is a parallelogram, we have to know the six characteristics of a parallelogram:
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect eachother.
One set of cogruent and parallel sides.
Definition: quadrilateral that has opposite sides parallel to eachother

14. Examples:
Yes, parallelogram.
We don’t have enough information to tell if it’s a parallelogram.
Yes, becuse the diagonals bisect eachother.

15. Rhombus + square + rectangle
Rhombus: It has 4 congruent sides and diagonals are perpendicular.

16. Square: It is equiangular and equilateral, it is both a rectangle and a rhombus and its diagonals are congruent and perpendicular.

17. Rectangle: Diagonals are congruent and has four right angles.
These three figures have in common that they are all parallelograms and have four sides.

18. Trapezoid and its theorems
A trapezoid is quadrilateral with one pair of parallel sides, each of the parallel sides is called a base and the nonparallel sides are called legs.
Base
legs

19. Theorems:
6-6-3: if a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent.
6-6-4: if a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles.
6-6-5: a trapezoid is isosceles if and only if its diagonals are congruent

20. Kite
A kite is a quadrilateral that has 2 pairs of congruent adjacent sides (2 lines at the top are congruent and the 2 lines at the bottom are congruent)
The properties:
Diagonals are perpendicular
One of the diagonals bisect the other
One pair of congruent angles (the ones formed by the non-congruent sides)

21. Kite Theorems:
6-6-1: if a quadrirateral is a kite, then its diagonals are perpendicular.
6-6-2: if a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.