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