Unit 1 Introduction
betweenness
A condition of one point being between two other points on a line.
bisector
A line or segment that intersects a segment at its midpoint.
collinear
Occurring on the same line.
coplanar
Occurring on the same plane.
geometry
From the Greek for "earth measure."
line segment
The set of two points and all points between.
midpoint
A point that divides a segment into two equal segments.
postulate
A statement accepted without proof.
opposite rays
and are opposite rays if A, B, and C are collinear and B (the endpoint of both rays) is between A and C.
ray
A ray, , is the set of all points from point A infinitely in the direction of point B.
space
The set of all possible points.
Unit 2 Logic
conclusion
The then clause in a conditional statement.
conditional or implication
Two statements connected by the form If ..., then....
conjunction
A statement formed by combining two statements with the word and.
contrapositive of a conditional
A statement formed by interchanging the hypothesis and the conclusion in a conditional statement, and negating both.
converse of a conditional
A statement formed by interchanging the hypothesis and the conclusion in a conditional statement.
deductive reasoning
Reasoning that leads from statement of a general fact to a specific conclusion
disjunction
A statement formed by combining two statements with the word or.
hypothesis
The if clause in a conditional statement.
inductive reasoning
The process of making a general conclusion based on specific examples.
inverse of a conditional
A statement formed by negating both the hypothesis and the conclusion in a conditional statement.
negation
If p is a statement, the new statement, not p or p is false is the negation of p.
statement
A theoretical declaration made in speech or writing; used to prove logical reasoning.
true-false statement
A sentence that is true or false, but not both.
Unit 3 Angles and Parallels
acute angle
An angle whose measure is less than 90°.
acute triangle
A triangle in which all three angles are acute.
adjacent angles
Two angles in the same plane that have a common vertex and a common side, but no interior points in common.
angle
The union of two noncollinear rays that have a common endpoint.
auxiliary line
A line introduced in a figure to make a proof possible. (Model 3)
bisector of an angle
A ray that is in the interior of the angle and divides the angle into two angles of equal measure.
complementary angles
Two angles with measures that, when added together, equal 90°. Each angle is called the complement of the other.
consecutive vertices
The endpoint of one side of a polygon.
consecutive sides
Any two sides of a polygon that have a common end point.
corollary
A statement that is easily proved by applying a theorem. (Model 4)
diagonal of a polygon
A segment joining two nonconsecutive vertices.
equiangular triangle
A triangle in which all angles are equal.
equilateral triangle
A triangle in which all three sides have the same length.
exterior angle of a triangle
An angle formed by one side of a triangle and the extension of an adjacent side of the triangle.
isosceles triangle
A triangle in which at least two sides have the same length.
obtuse angle
An angle with a measure greater than 90° but less than 180°.
obtuse triangle
A triangle in which one angle is obtuse.
parallel lines
Lines that are in the same plane and have no points in common. (| | lines)
parallel planes
Planes that have no point in common.
polygon
Any closed figure bounded by three or more segments that only intersect at their endpoints. The segments are called the sides and the endpoints are called the vertices of the polygon.
regular polygon
A polygon with all the angles equal and all the sides equal.
right angle
An angle whose measure equals 90°.
right triangle
A triangle in which one angle is a right angle.
remote interior angles
With respect to an exterior angle, the two interior angles of the triangle (Model 2).
scalene triangle
A triangle in which no two sides have the same length.
skew lines
Two lines that do not lie in the same plane.
supplementary angles
Two angles with measures that, when added together, equal 180°. Each angle is called the supplement of the other.
transversal
A line that intersects two or more coplanar lines in different points.
triangle
The union of three segments determined by three noncollinear points.
Unit 4 Congruent Triangles and Quadrilaterals
altitude of a triangle
A segment from a vertex perpendicular to the opposite side.
base angles
The two angles that include the base of an isosceles triangle.
base of an isosceles triangle
The third, unequal side of an isosceles triangle.
bases of a trapezoid
The parallel sides of a trapezoid.
congruent figures
If a one-to-one correspondence between the parts of two figures is such that the corresponding parts are equal, then the figures are congruent.
corresponding angles
Angles paired with one another in a one-to-one correspondence between geometric figures.
corresponding sides
Sides paired with one another in a one-to-one correspondence between figures.
included angle
The angle formed by two sides of a triangle.
included side
The side of a triangle formed by the common side of two angles.
isosceles trapezoid
A trapezoid with both legs of the same length.
legs of a trapezoid
The nonparallel sides of a trapezoid.
median of a trapezoid
The segment connecting the midpoints of the legs.
median of a triangle
A segment from a vertex to the midpoint of the opposite side.
one-to-one correspondence
The situation when each member of a set, such as angles of a triangle, can be paired with one and only one member of another set.
parallelogram
A quadrilateral with both pairs of opposite sides parallel.
rectangle
A parallelogram with four right angles.
rhombus
A parallelogram with all sides of equal length.
square
A rectangle with all sides equal and four right angles.
trapezoid
A quadrilateral with at least one pair of parallel sides.
vertex angle
The angle formed by the two equal sides of an isosceles triangle.
Unit 5 Similar Polygons
altitude of a triangle
An altitude of a triangle is a perpendicular line from a vertex to the opposite side.
cosine ratio
With respect to an acute angle of a right triangle, the ratio of the side adjacent to the angle over the hypotenuse.
diagonal of a rectangular solid
A segment whose endpoints are vertices not in the same face.
faces
The sides of a solid figure.
geometric mean
For any positive real numbers a, b, and x, if ax = xb then x is called the geometric mean between a and b. Notice that x2 = ab or x = \sqrt ab
Projection of a point on a line
the point where a perpendicular through the point to the line intersects the line.
Projection of a segment on a line
the portion of a line with endpoints that are the projections of the endpoints of the segment
proportion
An equation that states that two ratios are equal
ratio
The comparison of two numbers by division. The quotient is the ratio of the two numbers.
rectangular solid
A solid figure whose faces are all rectangles.
similar polygons ( ~ )
polygons whose vertices can be matched in 1:1 correspondence so that corresponding angles are equal and corresponding sides are in proportion.
sine ratio
With respect to an acute angle of a right triangle, the ratio formed by the side opposite the acute angle over the hypotenuse.
tangent ratio
With respect to an acute angle of a right triangle, the ratio of the side opposite the acute angle over the side adjacent to the acute angle.