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.•A polygon is any plane figure wth 3 or more sides•A concave polygon is a polygon that has angles pointing into the center of the figure.•A convex polygon is a polygon that has all of its vertices pointing out. •An equilanular polygon is a polygon with three congreunt angles.•An equidisitant is the same distance from two or more objects.

Explain the Interior angles theorem for quadrilaterals. Give at least 3 examples.

•The exterior anlges of every polygon have to add up to 360.•Polygon sum theorem (n-2)180= angle sum of any polygon

Describe the 4 theorems of parallelograms and their converse and explain how they are used. Give at least 3 examples of each.

•Any quadrilaterall with oppsite sides parallel to each other •opposite sides are also congruent •opposite angles are congruent to each other, •adjacent are suplementary.•The diagonals bisect each other.

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.

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 square is a quadrilateral with 4 congruent sides and 4 right angles.•A rhombus is a parallelogram that has 4 congruent sides•A rectangle is any parallelogran with 4 right angles.• if a quadrilaterall is a rhombus then it is a parallelogram•If a parallelogram is a rhombus then its diagonals are perpendicular ahd each diagonal bisects a pair of opposite angles•If a quadrilateral is a rectangle the it is a parallelogram and its diagonals are congruent

More examples….

Describe a trapezoid. Explain the trapezoidal theorems. Give at least 3 examples of each. 

• it is a quadrilateral with one set of parallel side opposite to each other.• An isoceles trapezoid is any trapezpoid with non parallel sides are congruent•If a quadrilaterall is an isocseles trapezoid the each pair of base angles are congruent.•A trapezoid is isosceles if and only if its diagonals are congruent •The midsegmens of a trapezoid is parallel to each base, and its length is one half the sum of the lenghts of the bases.•B1 + b2/ 2

More examples…

Describe a kite. Explain the kite theorems. Give at least 3 examples of each

•A quadrilateral that has two sets of congruent sides that are adjacent to each other.•The diagonals are perpendicular•One pair of opposite angles that are congruent.

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•Trapezoid A=a (b1+b2)/2•Kite Area = (½) d1d2•Area of rhombus = product of diagonals

Describe the 3 area postulates and how they are used. Give at least 3 examples of each.

•Area of a square postulate: the are of a square is the lenght of a square side •Area congruence postulate: if there are two closed figures that are congruent then they have the same area•Area adittion postulate: the area is the sum of the sum of the non overlaping parts