Basics of Geometry
What is the intersection of two lines?
A point
What is a conditional statement?
A logical statement with a hypothesis and conclusion.
Define skew lines
Two lines that never intersect and are in two different planes.
A triangle with one angle over 90 degrees and all sides unequal is classified as...
obtuse scalene
Two angles that add up to 90 degrees are...
complementary
What is the intersection of two planes?
A line
Given if p then q, what is the contrapositive statement?
If not q, then not p
Identify all pairs of angles formed by a transversal cutting through two lines.
Alternate interior, alternate exterior, corresponding and consecutive interior
Name the five ways to prove triangles are congruent
SAS, SSS, HL, ASA, AAS
When the sides of two angles form two pairs of opposite rays they are called...
vertical angles
Name the postulate that says:
If B is between A and C, then AB+BC=AC
Segment Addition Postulate
What are perpendicular lines?
Two lines that intersect to form a right angle.
If a line has slope m, what is the slope perpendicular to this line?
-1/m
Describe the exterior angle theorem
The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
What is the difference between a theorem and a postulate?
Theorem you can prove, postulate just is.
What is the distance formula?
sqrt of (x1-x2)+(y1-y2)
Name 3 properties of equality
Reflexive, Symmetric, Transitive
The converse theorems allow you to prove what?
How do we prove a part of a triangle is congruent to another part of a second triangle, if we know both triangles are congruent?
Corresponding Parts of Congruent Polygons are Congruent
What is the difference between inductive and deductive reasoning?
One is inferred, one is based on facts
What is the difference between a concave and convex polygon?
Concave all sides extended do not intersect the center of the polygon, concave the lines do
Name and describe the laws of logic.
Law of detachment-if hypothesis of a true conditional statement is true then the conclusion is true
Law of syllogism-If p then q, and q then r, therefore p then r
Find perpendicular slope to given line; find equation of line through given point and perpendicular to given line; find intersection of two lines, use distance formula.
What is the difference between base angles theorem and converse base angles theorem?
Base angles you know sides are congruent therefore you know base angles are congruent; converse you are given angles are congruent so then the sides are congruent.
In a proof, if you want to add congruent line segments, you have to...
convert congruence to measure