Download Majo D-DJournal 6

Journal 6
By: Maria Jose Diaz-Duran
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 closed figure formed
by 3 or more segments.
Convex
Concave
No points to the center of
the figure, no diagonal to the
exterior also a regular
polygon is always convex.
If it goes to the center of the
figure, contains points in the
exterior of a polygon
Equilateral
Equiangular
All sides are congruent
A polygon in which all angels
are congruent
Examples
Explain the Interior angles theorem
for quadrilaterals. Give at least 3
examples.
• The sum of the interior angle measures of a
convex polygon with n sides is (n-2)180
Examples
A. Find the sum of the interior angel measures of a convex octagon:
(n-2)180
(8-2)180
1080
B. Find the measures of each interior angle of a regular nonagon
Step 1: (n-2)180
(9-2)180
1260
Step 2: Find the measures of 1 interior angle
1260/9= 140
C. Find the measure of each interior angle of quadrilateral PQRS.
(4-2)180=360
M<p + M<Q + M<R +M<S=360
C+ 3C+ C+ 3C=360
8C=360
C=45
Describe the 4 theorems of parallelograms
and their converse and explain how they
are used. Give at least 3 examples of each.
Theorems
Converse
If a quadrilateral is a
parallelogram, then its
opposite sides are
congruent
If its opposite sides are
congruent, then a
quadrilateral is a
parallelogram
If a quadrilateral is a
parallelogram, then its
opposite angles are
congruent
If the opposite angles
are congruent, then a
quadrilateral is a
parallelogram
If a quadrilateral is a
parallelogram, then its
consecutive angles are
supplementary
If its consecutive angles
are supplementary then
a quadrilateral is a
parallelogram
If a quadrilateral is a
parallelogram, then its
diagonal bisect each
other
If its diagonals bisect
each other then a
quadrilateral is a
parallelogram
Examples
If a quadrilateral is a parallelogram, then its
opposite sides are congruent
If a quadrilateral is a parallelogram, then its
opposite angles are congruent
If a quadrilateral is a parallelogram, then its
consecutive angles are supplementary
If a quadrilateral is a parallelogram, then its
diagonal 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.
Theorems
If one pair of opposite sides of a quadrilateral are parallel and
congruent, then the quadrilateral is a parallelogram
If both pairs of opposite sides of a quadrilateral are
congruent then the quadrilateral is a parallelogram
If both pair of opposite angels of a quadrilateral are
congruent then then quadrilateral is a parallelogram.
Examples
If one pair of opposite sides of a quadrilateral
are parallel and congruent, then the
quadrilateral is a parallelogram
If both pairs of opposite sides of a
quadrilateral are congruent then the
quadrilateral is a parallelogram
If both pair of opposite angels of a
quadrilateral are congruent then then
quadrilateral is a parallelogram.
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.
Rectangle
Square
Rhombus
A quadrilateral with
four right angles.
A quadrilateral with
four right angles and
four congruent sides
A quadrilateral with
four congruent sides.
Theorems
Theorems
Theorems
If a quadrilateral is a
rectangle, then it is a
parallelogram
A quadrilateral is a
If a quadrilateral is a
square if and only if it rhombus then its is a
is a rhombus and a
parallelogram
rectangle.
If a parallelogram is a
rectangle then its
diagonals are
congruent
If a parallelogram is a
rhombus then its
diagonals are
perpendicular
If a parallelogram is a
rhombus, then each
diagonal bisects a
pair of opposite
angles.
Examples
Describe a trapezoid. Explain the
trapezoidal theorems.
Give at least 3 examples each
Trapezoid
A quadrilateral with exactly one pair of parallel sides, each of the parallel
sides is called a base and the nonparallel sides are called legs.
Theorems Isosceles Trapezoids:
if a quadrilateral is an isosceles trapezoid, then each pair of base angles are
congruent.
if a trapezoid has one pair of congruent base angles, then the trapezoid is
isosceles.
A trapezoid is isosceles if and only if its diagonals are congruent
Trapezoid Midsegment Theorems:
The midsegment of a trapezoid is parallel to each base and its length is one
half the sum of the lengths of the bases.
Examples
Describe a kite. Explain the kite
theorems. Give at least 3 examples of
each.
Kite
A quadrilateral with exactly two pairs of consecutive sides.
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.
Examples
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.
Describe how to find the areas of a square,
rectangle, triangle, parallelogram,
trapezoid, kite and rhombus. Give at least 3 examples
Areas:
of each.
Square
To find the area of a square, multiply
the lengths of two sides together
(XxX=X2)
Rectangle
To find the area of a rectangle, just
multiply the length times the width:
(LxW)
Triangle
1/2 xbxh or bxh/2
Parallelogram
To find the area of a parallelogram,
just multiply the base length (b) times
the height (h) (BxH)
Trapezoid
½ H(B+b)
Kite
To find the area of a kite, multiply the
lengths of the two diagonals and
divide by 2 (1/2AB)
Rhombus
To find the area of a rhombus,
multiply the lengths of the two
diagonals and divide by 2 (1/2AB)
Examples
Describe the 3 area postulates and
how they are used. Give at least 3
examples of each.
• 1. Area of a Square Postulate: The area of a
square is the square of the length of a side.
• 2. Area Congruence Postulate: If two closed
figures are congruent then they have the same
area.
• 3. Area Addition Postulate: The area of a
region is the sum of the areas of its nonoverlapping parts.
Examples
Area of a Square Postulate
Area Congruence Postulate
Area Addition Postulate