Notes

Postulates:

Corresponding Angles Postulate: If a transversal intersects two parallel lines, then corresponding angles are congruent.

Converse of the Corresponding Angles Postulate: If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel



Theorems:

Alternate Interior Angles Theorem: If a transversal intersects two parallel lines, then alternate interior angles are congruent

Same-Side Interior Angles Theorem: If a transversal intersects two parallel lines, then same-side interior angles are supplementary

Alternate Exterior Angles Theorem: If a transversal intersects two parallel lines, then alternate exterior angles are congruent

Same-Side Exterior Angles Theorem: If a transversal intersects two parallel lines then the same-side exterior angles are supplementary

Converse of the Alternate Interior Angles Theorem: If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel

Converse of the Same-Side Interior Angles Theorem: If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel

Converse of the Alternate Exterior Angles Theorem: If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel

Converse of the Same-Side Exterior Angles Theorem: If two lines and transversal form same-side exterior angles that are supplementary, then the two lines are parallel

Parallel Lines Theorem: If two lines are parallel to the same line, then they are parallel to each other

Perpendicular Lines Theorem: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

Perpendicular to Parallel Lines Theorem: In a plane, if a line is perpendicular to one of the two parallel lines, then it is also perpendicular to the other

Triangle Angle-Sum Theorem: The sum of the measures of the angles of a triangle is 180 degrees.

Triangle Exterior Angle Theorem: The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

Polygon Angle-Sum Theorem: The sum of the interior angles of a N-gon is (n-2)(180).

Polygon Exterior Angle-Sum Theorem: The sum of the measures of the exterior angles of a polygon, one at each vertex is is 360 degrees.

Defenitions:

Transversal: A line that intersects two coplanar lines at two distinct points

Alternate interior angles: Angles that are on the inside of lines cut by a transversal and on opposite sides of the transversal

Same-side interior angles: Angles that are on the inside of lines cut by a transversal and on the same side of the transversal

Corresponding angles: Angles that are in the same position with respect to the transversal

Alternate exterior angles: Angles that are on the outside of lines cut by a transversal and on opposite sides of the transversal

Same-side exterior angles: Angles that are on the outside of lines cut by a transversal and on the same side of the transversal

Triangles:

Equiangular: All angles are congruent
Acute: All angles acute
Right: One right angle
Obtuse: One obtuse angle
Equilateral: All sides congruent
Isosceles: At least two sides congruent
Scalene: No sides congruent
Exterior Angle of a Polygon: An angle formed by a side and an extension of an adjacent side

Remote Interior Angles: The two non-adjacent interior angles to a given angle

Polygon: A close figure with at least three sides that are segments. The sides intersect only at their endpoints and no adjacent sides are collinear

Naming Polygons: To name a polygon, start at any vertex and list the vertices consecutively in a clockwise or counterclockwise direction

Convex Polygon: A polygon that has no diagonals with points outside the polygon

Concave Polygon: A polygon that has at least one diagonal with points outside the polygon

Equilateral Polygon: A polygon in which all the sides are congruent

Equianglular Polygon: A polygon in which all the angles are congruent

Regular Polygon: A polygon that is both equiangular and equilateral

Slope-Intercept Form: y=mx+b Where m is the slope and b is the y intercept.

Standard Form of a Linear Equation: Ax+By=C Where A, B, and C are integers and A and B are not both equal to 0.

Point-Slope Form: y-y1=m(x-x1) Where m is the slope and (x1,y1) is a point on the line.