Download Chapter 8: Informal Geometry Section 8.3: Simple Closed Curves

Chapter 8: Informal Geometry
Section 8.3: Simple Closed Curves
Simple Closed Curves

Plane curve: a set of __________________ that can be drawn without ____________ the pencil

Simple: without lifting the ____________ , do not retrace ______ of its points

Closed curve: drawn by ___________ and ___________ at the same point

Jordan Curve Theorem: A simple closed curve c separates a plane into three disjoint sets of points
called the _________________, the _____________________, and the __________________ .

Region: Union of simple closed curve and its ___________________ .

Convex Region: a region is convex if, for ___________ two points in the region, the line segment
joining them lies __________________ in the region.

Nonconvex (concave) region: a region is concave if, for ___________ two points in the region, the
line segment joining them ______ ________ lie completely in the region.

Convex curves: Curves bounding convex regions are called ______________ ________________ .
Circles

Circle: the ___________ of _______________ points in a plane at a given distance from a fixed
_______________ in the plane is a ________________ .

Center: the fixed point in the _____________________ of a circle

Radius: a line ___________________ connecting the ____________________ to a point on the circle

Diameter: a line segment connecting ____________ points on the circle, containing the ____________

Chord: a line segment connecting _____________ points on the circle, ___________ containing the
diameter

Disk: the area of a circle plus the _____________________ of the circle
Polygons

Polygon: a ______________ is a simple _______________ curve that is the union of ______________
or more ____________ _______________________, such that __________ the points are coplanar and
_________________, no three ___________________ named points are collinear.

Sides: the line segments that form the ___________________ are called ______________

Vertices: the points defining the _______________ are called vertices

Adjacent vertices: endpoints on the ______________ side (line segment)

Diagonals: line segments joining _____________________________ vertices

Adjacent sides: sides with a common _______________________

Interior angles: we refer the _________________ of a convex polygon as the ______________ angles

Regular polygon: a simple _____________ polygon with __________ sides of _______________
length and all angles of _____________ measure is called a ___________________ polygon. Such a
polygon is said to be ____________________ and _____________________ .

Exterior angles: formed by extending one ________________ of a polygon and measuring the
_____________ formed; the interior angle and the ____________________ supplementary to each
other, their measures sum to ________ degrees
Regular Polygons or n-gons (n sides):
Name
Number of Sides
1. Triangle
3
Number of angles
3
2. Quadrilateral
4
4
3. Pentagon
______
5
4. Hexagon
6
6
5. Heptagon or 7-gon
7
______
6. Octagon
______
______
Triangles

Equilateral: all three sides are of ____________ length and all 3 angles are of equal ______________

Isosceles: at least _________ sides are congruent (have __________ length) ; the angles
______________ these sides are also congruent

Scalene: no two sides are ________________________ (no two sides have equal _____________ )
Quadrilaterals
Quadrilateral Definitions:
1. A parallelogram is a __________________ with both pairs of opposite sides _________________
2. A trapezoid is a quadrilateral with exactly _____________ pair of _______________ sides parallel
3. A rectangle is a parallelogram with a ___________________ angle. One right angle implies that all
_________ angles are ____________________ ________________________ .
4. A square is a ___________________ with all sides of _____________ length.
5. A rhombus is a ___________________ with all sides of ________________ length.
6. A kite is a quadrilateral with two distinct pairs of _________________ sides of _____________ length
Angles of Polygons

Interior angles – any polygon: may all be of ______________________ measures

Interior angles – regular polygon: are ALWAYS ____________________ measures

Central angle: formed by connecting the center of a _______________ polygon with a
_____________ of adjacent _______________
Angle Measures of Regular n-gons:
Number of sides Angle Sum
1.
3
1 ∙ 180°
2.
4
2 ∙ 180°
3.
5
3 ∙ 180°
4.
6
_______________
5.
n
_______________
Measure of Vertex Angle
(1∙180°)
= 60°
3
(2∙180°)
4
= 90°
____________________
____________________
Exercise Sets:
Homework:
p. 403: 1acegi, 2, 3ace, 4, 10, 11acegik, 12ace, 14ace, 19ac
Geogebra:
p. 403: 5ace, 6, 7ac, 8ace, 9aceg, 16, 17
Blazeview:
p. 403: 8, 13ac, 15, 36