JOURNAL 6Maria Elisa Vanegas 9-5

Polygons Parallelograms*Interior & Exterior Angles

*Theorems*Quadrilaterals

Rectangle

Square

Rhombus Trapezoid*Isosceles

POLYGONA Polygon is a closed figure that is formed by 3 or more straight segments.

Vocab:Sides of a Polygon= segment that forms a polygon.Vertex of the Polygon= common endpoints of 2 sides.Diagonal= a segment that connects any 2 non consecutive vertices.Equilateral= a polygon with all equal sides.Equiangular= a polygon with all equal angles.

CONCAVE Any figure that has 1 or more vertex pointing in.CONVEX Any figure that has all vertexes pointing out.REGULAR is one that is both equilateral and equiangular.

≠ regular = irregular

Number of sides

Name of polygon

34567891012#

TriangleQuadrilateralPentagonHexagonHeptagonOctagonNonagonDecagonDodecagon#-gon

Concave & Convex

Polygons

Regular & Irregular

Interior Angle theorem for Polygons=(n-2) x 180 By using this formula you will be able to found the sum of all the interior angles added together. If you want to find each interior angle then you divide the answer by the number of sides.

For all polygons the sum of the exterior angles is ALWAYS going to add up to 360⁰. If you want to find out each exterior angle then you divide the number of sides by 360.

Exterior Angle Sum theorem for Polygons=

PARALLELOGRAMA Parallelogram is a quadrilateral that has opposite sides parallel to each other OR it has 2 pairs of parallel sides.

1. Opposite sides are congruent2. Opposite angles are congruent3. Consecutive angles are supplementary4. Diagonals bisect each other5. 2 pairs of parallel sides6. One set of congruent and parallel sides

A Quadrilateral can be a Parallelogram if it has the following properties…

Parallelogram TheoremsIf a quadrilateral is a parallelogram then…1. Opposite sides are congruent.2. Opposite angles are congruent3. Consecutive angles are supplementary 4. Diagonals bisect each otherConverse…5. If the opposite sides of a quadrilateral are congruent then it is a

parallelogram.6. If the opposite angles in a quadrilateral are congruent then it is a

parallelogram.7. If the consecutive angles in a quadrilateral are supplementary then it

is a parallelogram.8. If the diagonals in a quadrilateral bisect each other then it is a

parallelogram.

RECTANGLEA Rectangle is any parallelogram with 4 right angle. Its diagonals are congruent.

RHOMBUSA Rhombus is a parallelogram with 4 congruent sides, in which its diagonals are perpendicular.

SQUAREA Square is a parallelogram that is both a rectangle and a rhombus. So it has 4 right angles, 4 congruent sides and angles, and its diagonals are perpendicular and congruent.

TRAPEZOIDTrapezoid= A quadrilateral with one pair of parallel sides.

Isosceles Trapezoid= is a trapezoid with a pair of congruent angles.

Properties of an Isosceles Trapezoid1. Diagonals are congruent 2. Base angles (both sets) are congruent3. Opposite angles are supplementary

Midsegment Theorem4. Midsegment= (b1+ b2) / 2 5. It is parallel to both bases6. It takes the same distance getting from base 1 to the midsegment and

from the midsegment to base 2.

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Isosceles Trapezoid

Midsegment

KITEKite= 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)

Properties of a kite1. Diagonals are perpendicular2. One of the diagonals bisect the other3. One pair of congruent angles (the ones formed by the non-congruent

sides)