Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
107 Cards in this Set
- Front
- Back
|
Conjecture
|
an unproven statement that is based on observations.
|
|
|
Inductive Reasoning
|
looking for patterns and making conjectures.
|
|
|
Counterexample
|
an example that shows a conjecture is false.
|
|
|
Definition
|
uses known words to describe a new word.
|
|
|
Undefined Terms
|
point, line, plane.
|
|
|
Point
|
has no dimension, and is represented by a small dot.
|
|
|
Line
|
extends in one dimension, represented by a straight line with arrowheads, and extends to infinity in both directions.
|
|
|
Plane
|
extends in two dimensions, is represented by a parallelogram, and extends to infinity, even though it appears to have edges.
|
|
|
Collinear Points
|
points that lie on the same line.
|
|
|
Coplanar Points
|
points that lie on the same plane.
|
|
|
Segment
|
a line that has a clear end and beginning.
|
|
|
Ray
|
a line that has one clear end and one that extends to infinity.
|
|
|
Opposite Ray
|
any pair of opposite rays forms a line--two rays that connect to each other.
|
|
|
Intersect
|
two or more geometric figures that have one or more points in common.
|
|
|
Intersection
|
the set of points the figures have in common.
|
|
|
Postulate/Axioms
|
rules that are accepted without proof.
|
|
|
Theorem
|
a rule that is proved.
|
|
|
Coordinate
|
a real number that corresponds to a point.
|
|
|
Distance
|
the absolute value of the difference between the coordinates.
|
|
|
Between
|
when three points lie on a line, you can say one is in "between" the other two.
|
|
|
Distance Formula
|
a formula for computing the distance between two points in a coordinate plane.
|
|
|
Congruent Segments
|
segments that have the same length.
|
|
|
Angle
|
consists of two different rays that have the same initial point.
|
|
|
Sides
|
the rays of the angle.
|
|
|
Vertex
|
the initial point of the angle.
|
|
|
Congruent Angles
|
angles that have the same measure.
|
|
|
Interior
|
the point of an angle if it is not on the angle or in its interior.
|
|
|
How are angles classified?
|
In categories according to their measures: acute, right, obtuse, and straight.
|
|
|
Adjacent Angles
|
two angles that share a common vertex and side, but have no common interior points.
|
|
|
Midpoint
|
the point that divides the segment into two congruent segments.
|
|
|
Bisects
|
divides.
|
|
|
Segment Bisector
|
a segment, ray, line, or plane that intersects a segment at its midpoint.
|
|
|
Straightedge
|
a ruler without marks.
|
|
|
Construction
|
a geometric drawing that uses a limited set of tools, usually a compass and a straightedge.
|
|
|
Midpoint Formula
|
taking the man, or average, of the x-coordinates and of the y-coordinates.
|
|
|
Angle Bisector
|
a ray that dives an angle into two adjacent angles that are congruent.
|
|
|
Vertical Angles
|
two angles that have sides from two pairs of opposite rays.
|
|
|
Linear Pair
|
two adjacent angles having non-common sides that are opposite rays--add up to 180 degrees.
|
|
|
Complementary Angles
|
two angles with the sum of their angles equaling 90 degrees--complementary to each other, can be adjacent or nonadjacent.
|
|
|
Supplementary Angles
|
two angles with the sum of their angles equaling 180 degrees--supplementary to each other, can be adjacent or nonadjacent.
|
|
|
Conditional Statements
|
two parts--hypothesis and a conclusion, written in if-then format.
|
|
|
If-Then Format
|
two parts--hypothesis and a conclusion, starts with "If..., then..."
|
|
|
Converse
|
formed by switching the hypothesis and conclusion.
|
|
|
Negation
|
writing the negative of the statement.
|
|
|
Inverse
|
negating the hypothesis and conclusion of a conditional statement.
|
|
|
Contra-positive
|
negating the hypothesis and conclusion of the converse of a condition statement.
|
|
|
Perpendicular Lines
|
intersecting to form a right angle.
|
|
|
Line Perpendicular to a Plane
|
a line that intersects the plane in a point and is perpendicular to every line in the plant that intersects it.
|
|
|
Bi-conditional Statement
|
a statement that contains the phrase "if and only if."
|
|
|
Logical Argument
|
facts, definitions, and accepted properties in a logical order.
|
|
|
Law of Detachment
|
If p -> q is true, and a conditional statement and p is true, then q is true.
|
|
|
Law of Syllogism
|
If p -> q and q -> r are true conditional statements, then p -> is true.
|
|
|
Addition Prop(=)
|
If a = b, then a + c = b + c.
|
|
|
Subtraction Prop(=)
|
If a = b, then a - c = b - c.
|
|
|
Multiplication Prop(=)
|
If a =b, then ac = bc.
|
|
|
Division Prop(=)
|
If a = b and c ≠ 0, then a ÷ c = b ÷ c.
|
|
|
Reflexive Prop(=)
|
For any real number a, a = a.
|
|
|
Symmetric Prop(=)
|
If a = b, then b = a.
|
|
|
Transitive Prop(=)
|
If a = b and b = c, then a = c.
|
|
|
Substitution Prop(=)
|
If a = b, then a can be substituted for b in any equation or expression.
|
|
|
Reflexive Prop(=)
|
For any segment AB, AB = AB.
|
|
|
Symmetric Prop(=)
|
If AB = CD, then CD = AB.
|
|
|
Transitive Prop(=)
|
If AB = CD and CD = EF, then AB = EF.
|
|
|
Theorem
|
a true statement that follows as a result of other true statements.
|
|
|
Two-Column Proof
|
a diagram with numbered statements and reasons that show the logical order of an argument.
|
|
|
Paragraph Proof
|
a proof written in paragraph form.
|
|
|
Parallel Lines
|
two lines that are coplanar and do not intersect.
|
|
|
Skew Lines
|
two lines that do not intersect and are not coplanar.
|
|
|
Parallel Planes
|
two planes that do not intersect.
|
|
|
Transversal
|
a line that intersects two or more coplanar lines at different points. It is classified by its sides and angles.
|
|
|
Classification by Sides: Equilateral Triangle
|
3 congruent sides.
|
|
|
Classification by Sides: Isosceles Triangle
|
At least 2 congruent sides.
|
|
|
Classification by Sides: Scalene Triangle
|
No congruent sides.
|
|
|
Classification by Angles: Acute Triangle
|
3 acute angles.
|
|
|
Classification by Angles: Equiangular Triangle
|
3 congruent angles.
|
|
|
Classification by Angles: Right Triangle
|
1 right angle.
|
|
|
Classification by Angles: Obtuse Triangle
|
1 obtuse angle
|
|
|
Vertex
|
each of the three points joining the sides of a triangle.
|
|
|
Adjacent Sides
|
two sides sharing a common vertex.
|
|
|
Right Triangle: Legs
|
the sides that form the right angle.
|
|
|
Right Triangle: Hypotenuse
|
the side opposite the right angle (in a right triangle).
|
|
|
Isosceles Triangle: Legs
|
When an isosceles triangle has only two congruent sides, then these two sides are LEGS of the isosceles triangle.
|
|
|
Isosceles Triangle: Base
|
The third side is the BASE of the isosceles triangle.
|
|
|
Interior Angles
|
the three original angles of a triangle.
|
|
|
Exterior Angles
|
The angles that are adjacent to the interior angles of a triangle.
|
|
|
Corollary to a Theorem
|
a statement that can be proved easily using the theorem.
|
|
|
Congruent
|
when two figures have a correspondence between their angles and sides so that the corresponding angles and corresponding sides.
|
|
|
Corresponding Angles
|
when the angles of a figure are all congruent.
|
|
|
Corresponding Sides
|
when the angles of a figure are all congruent.
|
|
|
Base Angles
|
the two angles adjacent to the base.
|
|
|
Vertex Angle
|
the angle opposite the base.
|
|
|
Coordinate Proof
|
involves placing geometric figures in a coordinate plane.
|
|
|
Perpendicular Bisector
|
a segment, ray, line, or plane that is perpendicular to a segment at its midpoint.
|
|
|
Equidistant from Two Points
|
a point that its distance from each point is the same.
|
|
|
Distance from a point to a line
|
the length of the perpendicular segment from the point to the line.
|
|
|
Equidistant from the two lines
|
when a point is the same distance from one line as it is from another line.
|
|
|
Perpendicular Bisector of a Triangle
|
a line (or ray/segment) that is perpendicular to a side of the triangle at the midpoint of the side.
|
|
|
Concurrent Lines
|
when three or more lines intersect in the same point.
|
|
|
Point of Concurrency
|
the point of intersection of the lines.
|
|
|
Circumcenter of the Triangle
|
the point of concurrency of the perpendicular bisectors of a triangle.
|
|
|
Angle Bisector of a Triangle
|
a bisector of an angle of the triangle.
|
|
|
Incenter of the Triangle
|
the point of concurrency of the angle bisectors.
|
|
|
Median of a Triangle
|
a segment whose endpoints are a vertex of the triangle and the midpoint of the poopsite side.
|
|
|
Centroid of the Triangle
|
the three medians of a triangle are concurrent; the point of concurrency is called the CENTROID.
|
|
|
Altitude of a Triangle
|
the perpendicular segment from a vertex to the opposite or to the line that contains the opposite side.
|
|
|
Orthocenter of the Triangle
|
the lines containing the altitudes are concurrent and intersect at a point.
|
|
|
Mid-segment of a Triangle
|
a segment that connects the midpoints of two sides of a triangle.
|
