Download math journal 6

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
If parallelogram then
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
• 6-4-3
• If a quadrilateral is a rhombus, then it is a
parallelogram
• 6-4-4
• If a parallelogram is a rhombus, then its
diagonals are perpendicular
• 6-4-5
• 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
• 6-4-1
• If a quadrilateral is a rectangle, then it is a
parallelogram
• 6-4-2
• If a parallelogram is a rectangle the its
diagonals are congruent.
6-4-1
rectangle
rectangle
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
• 6-6-3
• If a quadrilateral is and iscoceles
trapezoid, then each pair of base angles
are congruent
• 6-6-5
• A trapezoid is iscoceles if and only if its
diagonals are congruet
6-6-3
6-6-5
Kite
• It has two congruent adjecent sides and the
diagonals are perpendicular. Two pair of
congruent sides.
• Theorems:
• 6-6-1
• If a quadrilateral 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.
6-6-1
6-6-2