Unit 1
Line
-straight arrangement of points
-infinite amount of points
-infinite length but no thickness
-extends forever in both directions
P-->Q
Converse
Inverse
Contrapostive
Converse= Q -->P
Inverse= ~P -->~Q
Contrapositive= ~Q --> ~P
Parallel Lines
Perpendicular Lines
Skew Lines
Parallel: Lines that are co-planer but do not intersect.
Perpendicular: Lines that intersect to form a right angle.
Skew Lines: Lines that are not co-planer and do not intersect.
Triangle Sum Theorem
The sum of the measures of the angles of every triangle is 180o.
Ratio and Proportion
Ratio: A comparison of 2 numbers
Proportion: An equation of two equal ratios
Plane
-infinite length and width but no thickness
-has a flat surface that extends forever
Inductive Reasoning
-Observing data
-Looks for a pattern
-Makes a conjecture
-Proves it to always be true
Parallel Planes
Perpendicular Planes
Parallel Planes: Planes that do not intersect.
Perpendicular Planes: Planes that intersect to form a right angle.
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
Similar figures have:
Proportional corresponding sides and congruent corresponding angles.
Angle
-consists of two different rays that have the same initial point
Deductive Reasoning
-demonstrating that certain statements are accepted to be true, then other statements can be shown to follow from them.
Slope
Slope: m=rise/run = y2-y1/ x2-x1
Equiangular
Acute
Obtuse
Right
Equiangular:All 3 angles are congruent.
Acute: All 3 angles are acute.
Obtuse: One angles is obtuse.
Right: One angle is right.
Similar Figures Shortcuts
AA
SSS
SAS
Midpoint Formula
m= (x1+x2/2, y1+y2/2)
Law of Detachment (Modus Ponens)
P -->Q
P____
Therefore, Q
Alternate Interior Angles Theorem
IF two parallel lines are cut by a transversal, then pairs of alternate interior angels are congruent.
Equilateral
Isosceles
Scalene
Equilateral: All 3 sides are congruent.
Isosceles: At least 2 sides are congruent.
Scalene: No sides are congruent.
Indirect measurement
a method of using proportions to find unkown length or distance in similar figures.
Distance Formula
d=√(x2-x1)2 + (y2-y1)2
Law of Contrapositive (Modus Tollens)
P -->Q
~Q___
Therefore, ~P
Alternate Exterior Angles Theorem
IF two lines are cut by a transversal, then the pairs of the alternate exterior angles are congruent.
CPCTC!!!
Corresponding Parts of Congruent Triangles are Congruent!!!!!!
2 ways to find an object's height:
By using a mirror on the ground or by using shadow lengths.