Journal 6 Cristian Brenner

Polygons A polygon is a close figuire with straight sides that the line dont interset each other. With three or more segments

Parts of a Polygon Vertex: the vertex is where the segments of the polygon unite. Diagonals: are the segments that go from one vertex to the opposite vertex

Convex, Concave For a concave polygon the vertice are all facing outside and do not go in the figuire like a cave. In the convex all the vertices are facing out not in, the opposite of the concave

Equiangular, Equilateral Equilateral: This word is for when a polygon has all it sides congruent. Equiangular: When a polygons angles are all congruent. When a polygon is both it is a regular polyon if not it is irregular

Interior angles of Polygons This theorem says that that the sum of the interior angles of a convex is (n-2)180 (optional)and the answer divided by the number of sides to see how much is each angle.

Interior angles of polygons

6-2-1 If a quadrilateral is a parallelogram then its opposite sides are congruent Converse: If its opposite sides are congruent then its a parallelogram

6-2-1

6-2-1 converse

6-2-2 If a quadrilateral is a parallelogram, then its a opposite angles are congruent. Converse: If opposite angles are congruent then the quadrilateral is a parallelogram

6-2-2

6-2-2 converse

6-2-3 If a quadrilateral is a parallelogram, Then its consecutive angles are supplementary If the consecutive angles a of a quadrilateral are supplementery, then it is a parallelogram

6-2-3 If parallelogram then

6-2-3 converse

6-2-4 If a quadrilateral is a parallelogram the its diagonals bisect each other If diagonals bisect each other then its a parallelogram

6-2-4

6-2-4 converse

Prove quadrilateral is parallelogram You can know this when: Opposite angles are congruent Diagonals bisect Opposite sides are parallel and congruent Consecutive angles are supplementary

Proving quadrilateral as a parallelogram

Rhombus, Square, Rectangle The rhombus is somelike a square. All sides are congruent but angles change. It has all the characteristics of a parallelogram The rectangle changes in lenghts measure but all the angles are congruent as in the square. It has all the characteristics of a parallelogram

Rhombus Theorem If a quadrilateral is a rhombus, then it is a parallelogram If a parallelogram is a rhombus, then its diagonals are perpendicular If a parallelogram is a rhombus then each diagonal bisects a pair of oppsite angles

6-4-3

6-4-4

6-4-5

Rectangle Theorem If a quadrilateral is a rectangle, then it is a parallelogram If a parallelogram is a rectangle the its diagonals are congruent.

6-4-1 rectangle

6-4-2

Square It is a parallelogram which all its features are congruent

Trapezoid A polygon that has only two pair of parallel segments and sometime it is iscoceles, and when it is isco. Base angles and non parallel sides are congruent

Trapezoid Theorems If a quadrilateral is and iscoceles trapezoid, then each pair of base angles are congruent A trapezoid is iscoceles if and only if its diagonals are congruet

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6-6-5

Kite It has two congruent adjecent sides and the diagonals are perpendicular. Two pair of congruent sides. Theorems: If a quadrilateral is a kite, then its diagonals are perpendicular If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

6-6-1

6-6-2