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Journal chapter 6

Journal chapter 6. By Santiago Romero. Describe what a polygon is. Include a discussion about the parts of a polygon. Also compare and contrast a convex with a concave polygon. Compare and contrast equilateral and equiangular. Give 3 examples of each.

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Journal chapter 6

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  1. Journal chapter 6 By Santiago Romero

  2. Describe what a polygon is. Include a discussion about the parts of a polygon. Also compare and contrast a convex with a concave polygon. Compare and contrast equilateral and equiangular. Give 3 examples of each. • A polygonisanyplane figure wth 3 or more sides • A concavepolygonis a polygonthat has anglespointingintothe center of the figure. • A convexpolygonis a polygonthat has all of itsverticespointingout. • Anequilanularpolygonis a polygonwiththreecongreuntangles. • Anequidisitantisthesamedistancefromtwoor more objects.

  3. Explain the Interior angles theorem for quadrilaterals. Give at least 3 examples. • The exterior anlges of everypolygonhavetoadd up to 360. • Polygonsumtheorem (n-2)180= anglesum of anypolygon

  4. Describe the 4 theorems of parallelograms and their converse and explain how they are used. Give at least 3 examples of each. • Anyquadrilaterallwithoppsitesidesparalleltoeachother • oppositesides are alsocongruent • oppositeangles are congruenttoeachother, • adjacent are suplementary. • The diagonalsbisecteachother.

  5. Describe how to prove that a quadrilateral is a parallelogram. Include an explanation about theorem 6.10. Give at least 3 examples of each. 1) If a quadrilateral has one pair of sides that are both parallel and congruent, then the quadrilateral is a parallelogram. 2) If a the opposite sides of a quadrilateral are congruent, then then quadrilateral is a parallelogram. 3) Opposites sides are parallel. 4) Opposite angles are congruent 5) Diagonals bisect each other.

  6. Compare and contrast a rhombus with a square with a rectangle. Describe the rhombus, square and rectangle theorems. Give at least 3 examples of each. • a squareis a quadrilateralwith 4 congruentsides and 4 right angles. • A rhombusis a parallelogramthat has 4 congruentsides • A rectangleisanyparallelogranwith 4 right angles. • if a quadrilaterallis a rhombusthenitis a parallelogram • If a parallelogramis a rhombusthenitsdiagonals are perpendicular ahdeach diagonal bisects a pair of oppositeangles • If a quadrilateralis a rectangletheitis a parallelogram and itsdiagonals are congruent

  7. More examples….

  8. Describe a trapezoid. Explain the trapezoidal theorems. Give at least 3 examples of each. • itis a quadrilateralwithone set of parallelsideoppositetoeachother. • Anisocelestrapezoidisanytrapezpoidwith non parallelsides are congruent • If a quadrilaterallisanisocselestrapezoidtheeachpair of base angles are congruent. • A trapezoidisisoscelesif and onlyifitsdiagonals are congruent • The midsegmens of a trapezoidisparalleltoeach base, and itslengthisonehalfthesum of thelenghts of the bases. • B1 + b2/ 2

  9. More examples…

  10. Describe a kite. Explain the kite theorems. Give at least 3 examples of each • A quadrilateralthat has two sets of congruentsidesthat are adjacenttoeachother. • The diagonals are perpendicular • Onepair of oppositeanglesthat are congruent.

  11. Describe how to find the areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus. Give at least 3 examples of each. • rectangle A=lw • Square A=s2 • Triangle A=1/2 bh • Parallelogram A= bh • TrapezoidA=a (b1+b2)/2 • KiteArea = (½) d1d2 • Area of rhombus = product of diagonals

  12. Describe the 3 area postulates and how they are used. Give at least 3 examples of each. • Area of a squarepostulate: the are of a squareisthelenght of a squareside • Areacongruencepostulate: ifthere are twoclosed figures that are congruentthentheyhavethesamearea • Areaadittionpostulate: theareaisthesum of thesum of the non overlapingparts

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