Honors Geometry 5.1-5.3 Notes December 03-04, 2015
5.1 - 5.2 Notes
What if the Polygon is equiangular or regular?
Then one angle of an equiangular or regular polygon is...
Polygon Sum Formula:
Honors Geometry 5.1-5.3 Notes December 03-04, 2015
Examples
64
114 102 135
Note: This nonagon is regular.
x y
z
w
w = _______
x = _______
y = _______
z = _______
Honors Geometry 5.1-5.3 Notes December 03-04, 2015
Honors Geometry 5.1-5.3 Notes December 03-04, 2015
a
b
c
d
e
What is a + b + c + d + e ?
a b
c
de
Honors Geometry 5.1-5.3 Notes December 03-04, 2015
ab
cde
ab
cde
Honors Geometry 5.1-5.3 Notes December 03-04, 2015
So what is a + b + c + d + e ?
This is the Exterior Angle Sum Formula: For any polygon the sum of the
measures of a set of exterior angles is:
Set?
If our polygon is equiangular or regular then:
Each exterior angle is:
Each interior angle is:
Honors Geometry 5.1-5.3 Notes December 03-04, 2015
Examples:
1. What is the measure of one exterior angle in a regular pentagon?
2. If I know the interior angle of a regular polygon is 150 degrees. How many sides does the polygon have?
Missing Measurement: -Linear Pairs/supplementary angles-triangles int. angles total 180˚-isos. triangles: base angles are equal-sum of remote interior angles = the ext. angle of a triangle. -vertical angles are congruent-parallel line "stuff" -comp. angles-The sum of the angles around a common vertex is 360˚
NOW: Know SUM of interior and exterior angles of any polygon.
Honors Geometry 5.1-5.3 Notes December 03-04, 2015
What is a Kite?5.3-5.4 Notes
a quad. with two distinct pairs of consecutive congruent sides.
Kite Facts: 1. The nonvertex angles of a kite are___________________. 2. The diagonals of a kite are ___________________. 3. The diagonal connecting the vertex angles of a kite is the ________________ __________________ of the diagonal connecting the nonvertex angles. 4. The diagonal connecting the vertex angles of a kite ________________the vertex angles.
congruent
perpendicular
perpendicularbisector
bisects
Honors Geometry 5.1-5.3 Notes December 03-04, 2015
What is a trapezoid?
What is an isosceles trapezoid?
a quad. with exactly one pair of parallel sides.
a trapezoid whose non-parallel sides are congruent.
Bases
Consecutive angles between the bases
Pair of base angles
Pair of base angles
Trapezoid
Isosceles Trapezoid
Honors Geometry 5.1-5.3 Notes December 03-04, 2015
Trapezoid Fact: The consecutive angles between the bases of a trapezoid are ______________________
Isosceles Trapezoid Facts: 1. The base angles of an isosceles trapezoid are ____________________2. The diagonals of an isosceles trapezoid are ____________________
supplementary
congruent
congruent
17
31
Honors Geometry 5.1-5.3 Notes December 03-04, 2015
135
130
38
Honors Geometry 5.1-5.3 Notes December 03-04, 2015