Download Journal Chapter 6 gmorales(1).

Journal Chapter 6
By: Gabriel Morales
3 I want Corrected
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(0-10 pts.) 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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_____(0-10 pts.) Explain the Interior angles theorem for quadrilaterals. Give at least 3 examples.
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_____(0-10 pts.) Describe the 4 theorems of parallelograms and their converse and explain how they are used. Give at least 3 examples of each.
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_____(0-10 pts.) Describe how to prove that a quadrilateral is a parallelogram. Include an explanation about theorem 6.10. Give at least 3 examples of each.
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_____(0-10 pts.) 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.
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_____(0-10 pts.) Describe a trapezoid. Explain the trapezoidal theorems. Give at least 3 examples of each.
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_____(0-10 pts.) Describe a kite. Explain the kite theorems. Give at least 3 examples of each.
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_____(0-10 pts.) Describe how to find the areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus. Give at least 3 examples of each.
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_____(0-10 pts.) Describe the 3 area postulates and how they are used. Give at least 3 examples of each.
_____(0-10 pts.) Describe how to prove that a quadrilateral
is a parallelogram. Include an explanation about theorem
6.10. Give at least 3 examples of each.
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To do this we must know the definition of Quadrilateral is a 4 sided figure.
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A parallelogram has many properties to it
Def.: 4 sided figure with 2 sets of parallel lines
1.
All 4 opposite sides are congruent
2.
Opposite angles are congruent
3.
One pair of sides are parallel and congruent
4.
Diagonals Bisect
5.
Adjacent/ Consecutive angles are supplementary
6.
Theorem 6.10 states that if a quadrilateral is a parallelogram then its opposite sides are
congruent.
_____(0-10 pts.) 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.
Square:
All Sides are Right Angles
Equilateral and
Equiangular
Diagonals Bisect
Diagonals are
Perpendicular
Adjacent/Consecutive
Angles are supplementary
Rhombus:
All sides are
congruent
Diagonals are
Perpendicular
Rectangles:
A parallelogram with 4 right
angles
All < are right angles
Diagonals are Congruent
_____(0-10 pts.) Describe a trapezoid. Explain the
trapezoidal theorems. Give at least 3 examples of each.
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Trapezoid:
1. Both pairs of base angles are congruent
2. A quadrilateral with one pair of parallel
lines
3. Diagonals are Congruent
Iscoceles- Legs or 2 non parallel sides are
congruent
Midsegment Formula b1+b2
/2
_____(0-10 pts.) Describe a kite. Explain the kite
theorems. Give at least 3 examples of each.
 Kite:
One pair of congruent opposite sides.
Longer Diagonal bisects the shorter diagonal (Perpendicular)
One Pair of congruent opposite angles.
Theorems:
If a quadrilateral is a kite, then its diagonals are perpendicular
If a quadrilateral is a kite, then exactly one pair of opposite
angles are congruent.
_____(0-10 pts.) Describe how to find the areas of a square, rectangle,
triangle, parallelogram, trapezoid, kite and rhombus. Give at least 3 examples
of each.
Rectangle/ Square
BXH
Ex B 5 H5 Area = 25
B7 H7 Area = 49
H4 B 5 Area - 20
Parallelograms
BXH
Ex 5x 3 = 15
5 x 6 = 30
5 x 10 = 50
Area of top
triangle plus
bottom triangle
Triangle:
B X H /2
A = (5 x 6)/2= 15
A= 7 x 5 /2 = 17.5
A = 8 x 8 / 2 = 32
Trapezoid:
A= a (b1 + b2)
/2 a is the altitude
Rhombus
BXH
Ex B 5 H5 Area =
25
B7 H7 Area = 49
H4 B 54Area = 16
_____(0-10 pts.) 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.
 Polygons: polygons are closed figures made of 3 or more
straight lines.
 Polygons include sides, vertices, and diagonals
Sides: the sides are the points that meet at vertices.
Vertices: They are where the sides of the polygon meet
Diagonals: They are the imaginary lines that go from one of the
vertices to the opposite angles.
Concave
 Concave polygons are those who have an interior angle that is
more than 180 degrees. Or a side that goes inside the
polygon. (angles push in)
Convex
 Convex is when no interior angles push in.
Equiangular
All angles are the same! Like in a square or rectangle!
Equilateral
 All sides are congruent! Like in a rhombus, a square!
_____(0-10 pts.) Explain the Interior angles theorem for
quadrilaterals. Give at least 3 examples.
How many sides are there?Then subtract 2 from the # of
sides…Then multiply by 180 to find the degrees of the
quadrilateral!
Ex Rhombus has 4 sides so go 4-2 times 180 which equals 360!!
5 – 2 x 180 = 540
Ex 3-2 x 180 = 180!
4 theorems of Parallelograms
When one pair of opposite sides of a quadrilateral are
congruent and parallel, then the quadrilateral is a
parallelogram
Converse: it is a parallelogram if if a pair of opposite sides are
congruent and parallel.
2nd
When both pairs of opposite sides of quadrilaterals are
congruent the quadrilateral is a parallelogram
Converse: It is a parallelogram if both of the opposite sides are
congruent.
3rd
When an angle of a quadrilateral is supplementary to both of its
consecutive angles, then the quadrilateral is a parallelogram
Converse: It is a parallelogram if the angle is supplementary to
both of its consecutive angles.
4th
 When the diagonals of a quadrilateral bisect each other, then
the quadrilateral is a parallelogram
 Converse: It is a parallelogram if the diagonals bisect each
other