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Section 2-1
Triangles

Triangle- three sides, three angles

Theorem 2-1 Triangle angle sum: The sum of the measures of the angles of a triangle is one hundred eighty degrees
m
Exterior angle- is an angle formed by a side and an extension of a side
Remote- for each exterior angle of a triangle, the two non-adjacent interior angles

Theorem 2-2 Exterior angle: The measure of each exterior angle of a triangle equals the sum of the measure of its two remote

Interior angles
m<1= m<2 + m<3

Corollary to Theorem 2-2: The measure of an exterior angle of a triangle is greater than the measure of either of its remote

Interior angles
m<1 > m<2 and m<1 > m<3

Classifying Triangles

Equilateral= all sides congruent
Isosceles= at least two sides congruent
Scalene= no sides congruent
Equiangular= all angles are congruent
Acute= all angles are acute
Right= one ninety degree angle
Obtuse= on obtuse angle

Section 2-2
Polygons

Polygons- many sides, closed plane figure with at least three sides
Concave- caves inward, if any diagonal contains Points outside the polygon, then its concave
Convex- no diagonal points outside polygon, no exit

Types of polygons

Triangle- 3 sides
Quadrilateral- 4 Sides
Pentagon= 5 sides
Hexagon= 6 sides
Heptagon= 7 sides
Octagon= 8 sides
Nonagon= 9 sides
Decagon= 10 sides
Do Decagon= 12 sides
N-gon= n sides

Theorem 2-3 polygon interior angle sum: The sum of the measures of the interior angles of an n-gon is (n-2)180
Theorem 2-4 polygon exterior angle sum: the sum of the measures of the exterior angles of a polygon, one at each vertex, is 360 degrees

Sections 2-3
Parallel and Perpendicular lines

Theorem 2-5: Two lines parallel to a third are parallel to each other
Theorem 2-6: In a plane, two lines perpendicular to a third are parallel to each other

Slope-Pitch or steepness of the line
Slope Formula=

Parallel Lines- lines that have the same slope
Perpendicualr Lines- lines that have the same slopes that are negative reciprocals

Classifying Quadrilaterals
Parallelograms- opposite lines are parallel
Rhombus- a parallelogram with 4 right congruent sides
Rectangle- a parallelogram with 4 right <'s and 4 congruent sides
Kite- a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent
Trapezoid- a quadrilateral with exactly one pair of parallel sides
Isosceles trapezoid- a trapezoid whose non parallel sides are congruent

Section 2-5
Circles

Circle- set of all points in a plane equidistant from a given point, called the center
Radius- is a segement that has one endpoint at the center and the other endpoint on the circle
Diameter- is a segment that contains the center of the circle and both endpoints on the circle.
Always cuts the cirlce in half

central angle- angle whose vertex is the center of the circle

Diameter= 2r

Arcs- a part of a circle

3 Types of circles
1. Semi circle= 180 degrees half a circle
2. Major arcs= longer than the semi circle
3. Minor arcs= shorter than the semi circle


Section 2-6 Congruent and Similar Figures

Congruent figures have exactly the same size and shape.
Congruent circles have a ~ radi.

Congruent Polygons have a ~ corresponding parts. (Corresponding parts matching angles and side.

When naming congruent polygons always list corresponding vertices in the same order.
Similar Polygons
Two figures that have the same shape but not nessarily the same similar ~ symbol

Two polygons are similar if :

1. The corresponding angles are congruent.

2. The corresponding sides are proportional

The ratio of a corresponding side is the similarity ratio.

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Section 3-1 Thru 3-7