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Parallel Lines  coplanar lines that don't intersect

Skew Lines  noncoplanar lines that don't intersect

Parallel planes  planes that don't intersect

Transversal a line that intersects two or more coplanar lines at different points


Alternate exterior angles
* If the the alternate exterior angles are congruent, then the lines are parallel.

* If two parallel lines, then the alternate interior lines are congruent.
* If the alternate interior angles are congruent, then the lines are parallel.

Corresponding angles

* If two parallel lines, then the corresponding angles are congruent.
* If the corresponding angles are congruent, then the lines are parallel.
* Corresponding angles are congruent.


* If two parallel lines, then the SSInt angles are supplementary.
* If the SSInt angles are supplementary then the lines are parallel.
* Same Side Interior angles are supplementary (180°)

If two parallel lines, then the alternate exterior angles are congruent.
Alternate exterior angles are congruent

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other

In a plane if two lines are perpendicular to the same line then the lines are parallel

In two lines are parallel to the same line then the lines are parallel

Through a point outside a line there is exactly one line parallel or perpendicular to the given line

Angle Sum Theorem
the sum of the angles of a triangle is 180 degrees

Corollaries statement easily proven by applying a theorem

Third Angle Theorem
If two angles in one triangle are congruent to two angles in another triangle then the third angles are congruent.

The acute angles of a right triangle are complementary (90°)

Classifying Triangles by SIDES:
Scalene: no equal sides, no equal angles
Isosceles: two equal sides, two equal angles
Equilateral: three equal sides, three equal angles always 60°

Scalene: no equal sides, no equal angles

Isosceles two equal sides, two equal angles

Equilateral three equal sides, three equal angles always 60°

Classifying triangles by ANGLES:
* Right triangle has a right angle (90°)
* Acute triangle all angles are less than 90°
* Obtuse triangle has an angle more than 90°
* Equiangular triangle has all angles measuring 60°.

Right triangle has a right angle (90°).

Acute triangles: all angles are less than 90°

Obtuse triangle has an angle more than 90°.

Equiangular
Each angle in a equiangular triangle is 60°.

There can be at most one right angle or obtuse angle in a triangle

Exterior angle of triangle an angle that forms a linear pair with an interior angle of a triangle

remote interior angles the two angles in the triangle that are nonadjacent to the exterior angle

Exterior Angle Theorem the measure of the exterior angle of a triangle is equal to the sum remote interior angles.

polygon
* 2 dimensional
* only segments
* intersects at end points

convex
* lines contain closed sides
* dont contain points
nonconvex
* concave


3 sides  triangle
4 sides  quadrilateral
5 sides  pentagon
6 sides  hexagon
7 sides  hectoton
8 sides  octagon
9 sides  nonagon
10 sides  decagon
n sides  whatever number of sides

regular polygon
* equilateral and equilangular
* congruent sides and all angles are congruent

diagonal a segment joining nonconsecutive vertices of the polygon

Interior Angle Sum Theorem
the sum of the interior angles of a convex polygon interior angle sum is (n2)180

To find interior angle in regular octagon.
Interior angle = (n2)180/n

Exterior Angle Sum Theorem
the sum of the exterior angles, one angle at each vertex, of a convex polygon is always 360°.

each exterior angle = 360/n

