Download mate ch. 6

Journal Chapter 6
FRANCIS MIFSUD
T2
_____(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. (angles push in)
Concave
polygon
The Yellow angle make these polygons concave
Convex
 Convex is when no interior angles are larger than 180
degrees (no angles push in)
No angles are larger than 180 degrees which makes the polygons convex
Equiangular
 Equiangular are seen in many places like in boxes and
stop signs
STO
P
Equilaterals
 Equilaterals are used in many square objects like
rhombuses.
_____(0-10 pts.) Explain the Interior angles theorem for quadrilaterals.
Give at least 3 examples.
The interior angles theorem for quadrilaterals works like
this….
How many sides are there?
Then subtract 2 from the #
of sides…
Then multiply by 180 to
find the degrees of the
quadrilateral!
(4-2)180= 360
 The theorem says that (n-2)180… n being the number of
sides.
(4-2)180=360
(4-2)180=360
Describe the 4 theorems of parallelograms and their converse and
explain how they are used. Give at least 3 examples of each.
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.
This is an easy way to see if a quadrilateral is a
parallelogram because you only need to find the
length of the sides and if their they are perp. To
each other then you can see they are parallel
Second Theorem
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.
This is easy to use because if you
know all the lengths you can find
if it is a parallelogram
Third…
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.
If the meeting angles are
supplementary then they it is
a parallelogram
This is helpful because sometimes
you are given the angles and you
can see if they are supplementary
Fourth…
 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
Describe how to prove that a quadrilateral is a parallelogram. Include an
explanation about theorem 6.10. Give at least 3 examples of each
 First you have to know the definition of Quadrilateral is a 4
sided figure.
 And that a parallelogram has many properties to it
Def.: 4 sided figure with 2 sets of parallel line
1.
First you have need to know that opposite angles are
congruent
2.
Second you need find one pair of sides are parallel and
congruent
3.
Then show that diagonals Bisect
4. Then show that adjacent/ Consecutive angles are
supplementary
5. At last with theorem 6.10 that states that if a
quadrilateral is a parallelogram then its opposite sides
are congruent, show that it is a parralelogram
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 angles are right angles
Diagonals are Congruent
Describe a trapezoid. Explain the trapezoidal theorems. Give at least 3
examples of each.
 A trapezoid is a quadrilateral with 2 base sides that are
parallel to each other
 Some properties of a trapezoid are:
1. Both pairs of base angles are congruent
2. A quadrilateral with one pair of parallel lines
3. Diagonals are Congruent
Theorems of a Trapezoid
 Isosceles- Legs or 2 non parallel sides are congruent
 Midsegment Formula b1+b2/2
Describe a kite. Explain the kite theorems. Give at least 3 examples of
each.
 A Kite is composed of two figures tor two triangles that
make a polygon with bisecting diagonals
 Properties:
One Pair of congruent opposite angles
One pair of congruent opposite sides.
Longer Diagonal bisects the shorter diagonal
(Perpendicular)
Theorems
Theorems:
If a quadrilateral is a kite, then exactly one pair of
opposite angles are congruent.
If a quadrilateral is a kite, then its diagonals are
perpendicular
Describe how to find the areas of a square, rectangle, triangle,
parallelogram, trapezoid, kite and rhombus. Give at least 3 examples of
each.
 Trapezoid:
 A= a (b1 + b2)
/2 a is the altitude
 Rhombus: base times height
 Parallelograms: baste time height
 Rectangle/ Square: base times height
 Kite : area of top triangle plus area of bottom triangle
 Triangle: base times height /2