Geometry Final Exam Review
CPCTC
"Corresponding Parts of Congruent Triangles are Congruent"
Opposite rays
2 rays that travel in opposite directions and have the same endpoint
Plane
A 2-D flat surface that extends infinitely in all directions
Polygon
A closed figure with three or more sides
Inverse
A conditional statement where you negate the hypothesis and the conclusion (~p→~q)
Regular polygon
A convex polygon with all sides and angles congruent
Transversal
A line that intersects two coplanar lines at two distinct points
Rhombus
A parallelogram with four congruent sides
Square
A parallelogram with four congruent sides AND four right angles
Rectangle
A parallelogram with four right angles
Ray
A part of a line consisting of one endpoint and all the points on one side of that point
Segment
A part of a line consisting of two endpoints and all points between those two points
Midpoint
A point that divides a segment into two congruent segments (in other words, this point bisects the segment)
Vertex
A point that is the endpoint to an angle
Equiangular polygon
A polygon that has all angles congruent (just all angles congruent, not all parts congruent)
Equilateral polygon
A polygon that has all sides congruent
Triangle
A polygon with 3 sides
Substitution property
A property of congruence and equality that looks like: If a=b, then b may replace a in any expression.
Symmetric property
A property of congruence and equality that looks like: If ⦣A≅⦣B, then ⦣B≅⦣A
Transitive property
A property of congruence and equality that looks like: if a=b and b=c, then a=c
Reflexive property
A property that can show equality or congruence. an example: ⦣A≅⦣A or AC=AC
Parallelogram
A quadrilateral with BOTH pairs of opposite sides parallel
Trapezoid
A quadrilateral with EXACTLY one pair of parallel sides
Kite
A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent
Line
A set of points that extend in opposite directions infinitely
Point
A specific location in space that is infinitely small
Conditional
A statement in "if-then" form (p→q)
Isosceles trapezoid
A trapezoid whose nonparallel opposite sides are congruent
Equiangular triangle
A triangle that has all angles congruent
Equilateral triangle
A triangle that has all sides congruent
Scalene triangle
A triangle who has no congruent sides
Acute triangle
A triangle with acute angles
Isosceles triangle
A triangle with at least two sides congruent
Obtuse triangle
A triangle with one angle greater than 90°
Right triangle
A triangle with one right angle
Two-column proof
A type of proof that consists of statements and reasons.
Postulate
Also called an axiom; an accepted statement of fact
Vertex angle of an isosceles triangle
An angle across from the base in an isosceles triangle
Straight angle
An angle who has the measure of 180°
Alternate exterior angles
Angles that lie on the exterior of parallel lines (on opposite sides of the transversal) and are congruent when a transversal intersects the two parallel lines
Alternate interior angles
Angles that lie on the interior of parallel lines (on opposite sides of the transversal) and are congruent when a transversal intersects the two parallel lines
Obtuse angle
Any angle greater than 90° and less than 180°
Acute angle
Any angle whose measurement is less than 90°
Truth value
Because of this, a statement is determined to be either true or false. In order to be true, a statement must always be true without any counterexamples. In order to be false, a statement needs at least one counterexample.
Parallel lines
Coplanar lines that never intersect
Converse
Do you use the regular or the converse of the angle theorems when you are given angle relationships and trying to parallel lines? (or in simple form, ∠'s → ║=?)
Regular
Do you use the regular or the converse of the angle theorems when you are given parallel lines and are trying to prove angle relationships? (or in simple form, ║ → ∠'s = ?)
Distributive property
Example of this property: If a(b+c), then ab +ac.
Point-Slope form (of a linear equation)
Form of a linear equation that looks like: y-y₁=m(x-x₁)
Slope-intercept form (of a linear equation)
Form of a linear equation that looks like: y=mx+b
Angle
Formed by two rays with the same endpoint
Distance formula
Formula used to find the distance (sometimes on a coordinate plane, but most of the time on a segment). the formula is d= √(x₂-x₁)²+(y₂-y₁)²
Midpoint formula
Formula used to find the midpoint (sometimes on a coordinate plane, but most of the time on a segment). the formula is M (x₁+x₂/2, y₁+y₂/2). "M" refers to point M (the midpoint). Find AB means find the distance between A and B.
Law of detachment
If a conditional is true and its hypothesis is true, then its conclusion is true
Law of syllogism
If p→q is true AND q→r is true, Then p→r is true
Perpendicular lines
Lines that intersect to form right angles
Parallel planes
Planes that do not intersect
Congruent segments
Segments who have the same length
Same-side exterior angles
Supplementary angles on the same side of the transversal and on the exterior
Same-side interior angles
Supplementary angles on the same side of the transversal and on the interior
Hypothesis
The "if" part of a conditional statement (p)
Conclusion
The "then" part of a conditional statement (q)
Hypotenuse
The longest side of a right triangle
Exterior angle of a polygon
The measure of one of these is found by taking 360°/number of sides. The sum of all of these kinds of angles on a regular polygon ALWAYS equals 360°.
Deductive reasoning
The process of reasoning logically from given statements to a conclusion
Space
The set of all points
Legs of an isosceles triangle
These are the only two sides of an isosceles triangle that are congruent
Vertical angles
Two angles whose sides form two pairs of opposite rays; these angles are congruent.
Supplementary angles
Two angles whose sum is 180°
Remote interior angles
Two nonadjacent angles within a triangle to a given exterior angle (these two angles added together are equal to the exterior angle)
Conjecture
a conclusion reached using inductive reasoning; an educated guess
Perpendicular bisector
a line, segment, or ray that is perpendicular to the segment at its midpoint... thereby bisecting the segment into two congruent segments.
Convex polygon
a polygon where all diagonals are in the interior
Concave polygon
a polygon with one or more points of a diagonal not in the interior
Angle bisector
a ray that divides an angle into two congruent coplanar angles
Coordinate
a set of numbers that determines the location of a point in space
Theorem
a statement that can be proved to be true
Corollary
a statement that follows directly from a theorem
Contrapositive
a statement where you switch AND negate the hypothesis and conclusion. **If a conditional statement is true, then this will always be true for it as well.** (~q→~p)
Converse
a statement where you switch the hypothesis and conclusion (q→p)
Compass
a tool used in geometry for constructions.
Straight edge
a tool used to construct straight lines, segments, edges, etc.
Axiom
also called a postulate; an accepted statement of fact
Biconditional
an "if and only if" statement; both conditional and converse are true, p↔q,
Right angle
an angle whose measure is exactly 90°
Counterexample
an example that shows a conjecture is false or wrong
Base angles of an isosceles trapezoid
angles in an isosceles trapezoid that are congruent
Base angles of an isosceles triangle
angles in an isosceles triangle that are congruent
Corresponding angles
angles that lie on the same side of the transversal and are congruent. One is on the interior, one is on the exterior.
Congruent angles
angles who have the same measure
a=s² (where s= the length of one side)
area of a square
Skew lines
noncoplanar lines that do not intersect
p=4s
perimeter of a square
Coplanar
points and lines that lie on the same plane
Collinear points
points that lie on the same line
Congruent polygons
polygons that have congruent corresponding parts
Inductive reasoning
reasoning based on generalizations made when looking at patterns
Base of an isosceles triangle
the noncongruent side of an isosceles triangle
Complementary angles
two angles whose measures have a sum of 90°
Adjacent angles
two coplanar angles with a common side, a common vertex, and no common interior points