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