Journal Chapter 6 Javier Mendez
Dec 30, 2015
PolygonsA polygon is any shape that is closed, has more than two sides and it does not have curved sides. In a polygon, the segments cannot intersect each other.
Every polygon has sides vertices and they may have diagonals.
diagonal
side
vertex
Not a Polygon
When a polygon has a vertex pointing in, it is a concave polygon.
The flag of Nepal is a concave polygon.
When all of the vertices are pointing outside, it is a convex polygon.
These figures are convex polygons.
Convex
Equilateral: When all of the sides of a polygon are congruent.
Equiangular: When all of the angles of a shape are congruent.
Interior Angles TheoremThe sum of the interior angles of a convex polygon will always be the number of sides the polygon has, minus 2 times 180.
Octagon 8 – 2 = 6 6 x 180 = 1080
1080 degrees
The sum of a 100-gon is: The sum of a 78-gon is:
100 – 2 = 98 x 180 = 17640 degrees 78 – 2 = 76 x 180 = 13680 degrees
ParallelogramsA parallelogram is a shape that has two pairs of parallel sides in it.
Properties of Parallelograms:
1) In a parallelogram, opposite sides are congruent.2) In a parallelogram, opposite angles are congruent.3) In a parallelogram, consecutive angles are supplementary.4) In a parallelogram, diagonals bisect each other.
AB
C D
B = D A = C
How to Prove that Quadrilaterals are
ParallelogramsIf a quadrilateral has one pair of congruent and parallel sides, it is a parallelogram.
*The rest of the reasons where shown previpusly.
Tell if the following quadrilaterals are parallelograms:
A
B
C
D
E
GIVEN:DE= 48EB= 49
IT IS NOT A PARALLELOGRAM
A
B
C
D
GIVEN:DB ll AB
YES IT IS
A
B C
D GIVEN:AD ll BC
IT IS NOT A PARALLELOGRAM BECAUSE WE DON’ T KNOW IF THEY ARE CONGRUENT.
A
BC
DGIVEN: X = 10ANGLE D = X * 9 + 5ANGLE B = 85 + XANGLE C AND A ARE CONGRUENT TO EACH OTHER.
IT IS A PARALLELOGRAM
Rhombus, Squares and Rectangles
A rectangle is a quadrilateral with 4 right anglesA rectangle is a parallelogramIts diagonals are congruent
A rhombus is a qudrilateral with 4 congruent sidesIt is a parallelogram Its diagonals are perpendicularDiagonals bisect a pair of opposite angles
A square is a quadrilateral with all of the sides congruent and all of the angles tooIt is a rectangle, a rhombus and a parallelogram.
Tell if the following shapes are squares, rectangles or rhombus
AB
CD
GIVEN:CA = DB
RECTANGLEA
B
C
DGIVEN:ANGLE A AND D ARE 45
IT IS A RHOMBUS
GIVEN: ONE OF THE ANGLES = 90
IT IS A SQUARE
Trapezoids
A trapezoid is a quadrilateral that has a pair of parallel sides.In an isosceles trapezoid the pairs of base angles are congruent.When a trapezoid has a pair of congruent base angles, it is isoscelesWhen a trapezoid is isosceles, it has congruent diagonalsThe midsegment of a trapezoid is parallel to both bases and its lenght is one half of the sum od the lenghts of the bases.
Is it isosceles?
Yes
Is this an isosceles trapezoid?
A
C
D AC > BD
NO
B
28
WHAT IS THE SUM OF THE TWO BASES?
56
THE SUM OF THE BASES IS 100, WHAT IS THE LENGHT OF THE MIDESEGMENT?
50
KitesA kite is quadrilateral with two pairs of consecutive congruent sides.Its diagonals are perpendicularOne pair of opposite angles is congruent.
IS THIS A KITE?
YES
IS THIS A KITE?
NO26
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