Larson Geometry Reference – Chapter 1
Definitions
Term/Concept / Description*Adjacent / Adjacent angles are angles that share a common vertex and a common side but have no points in common in the interior. Adjacent sides are sides that share a common vertex.
In simple terms, adjacent means “next to”.
*Angle / The union of two rays having the same end point. The end point is called the vertex of the angle, and the rays are called the sides of the angle.
Angle, Acute / An angle with a measure less than 90 degrees
Angle, Obtuse / An angle with a measure greater than 90 and less than 180
Angle, Reflex / An angle greater than 180 and less than 360.
Angle, Right / An angle with a measure of exactly 90.
Angle, Straight / An angle with a measure of 180. A straight line.
Angles, Adjacent / Two angles that share the same vertex, share a common side and do not overlap.
*Angles, Complementary / Two angles whose measures add to 90.
*Angles, Linear Pair / Adjacent angles whose non-common sides are opposite rays.
*Angles, Supplementary / A pair of angles whose measures add to 180.
*Angles, Vertical / Two angles whose sides form two pairs of opposite rays.
Betweenness / A point P is between points A and B if points A, P and B are collinear points, and if .
Bisector, Angle / A ray, line, or segment that divides an angle into two congruent angles.
Bisector, Line Segment / Any line, ray, or segment that passes through the midpoint of the segment. A segment bisector divides a segment into two congruent segments.
Collinear, Non-Collinear Points / Collinear points are points that lie on the same line. Non-collinear points are points that do not lie on the same line.
Congruent, Angles / Angles are congruent if their measures are equal. Also if angles have equal measures then they are congruent.
*Congruent, Segments / Line segments are congruent if their lengths are equal. Also if line segments have equal lengths then they are congruent.
*Coplanar, Non-Coplanar / Coplanar objects are objects that lie in the same plane. Non-coplanar objects are objects that do not lie in the same plane.
Equiangular / A polygon in which all interior angles are congruent.
*Equilateral / A polygon in which all sides are congruent.
Intersection / The intersection of two objects is the set of points that are contained in both objects.
Line / A straight object that is infinitely long and infinitely thin. A line has no width and no thickness, only length. A line may contain an infinite number of points but it must have at least two. A line is denoted by naming two points on the line with a line over the letters with arrows pointing in either direction. .
*Line Segment / A part of a line consisting of two points called end points, and the set of all points between the end points. A line segment is denoted as where A and B are the end points.
*Midpoint / A point that cuts a line segment into two congruent segments.
Opposite Rays / Rays with the same endpoint and point in opposite directions. Opposite rays form a line,
Plane / A two dimensional object that is infinitely large. Planes have no thickness only length and width. Planes are named with the word plane followed by three non-collinear points, or by the word plane followed by a single letter.
Point / A point indicates position. Since it is a place and not a thing, it has no dimension. It has no length, width, or depth. Points are usually named by a single capital letter.
*Polygon / A closed, coplanar figure made up of 3 or more line segments connected end-to-end.
Polygon, Concave / A polygon such that at least one line containing a side of the polygon contains a point in the interior of the polygon.
Polygon, Convex / A polygon such that no line containing a side of the polygon contains a point in the interior of the polygon.
Definitions(Cont.)
Term/Concept / DescriptionPolygon, Regular (ch. 7) / A convex polygon that is both equilateral and equiangular.
Postulates / Basic assumptions that are accepted as true and do not require proof. Also known as axioms.
*Ray / A part of a line that starts at an end point goes to infinity in one direction. A ray is denoted using two points, the end point and some other point on the ray with an arrow over them in one direction .
Terms, Defined / Terms that can be combined with other term to make new terms.
Terms, Undefined / Terms that are fundamental and can not be defined using simpler terms. They can only be described. Point, line, and plane are undefined terms
*Vertex / The point at which line segments, lines or rays intersect in a 2 or 3 dimensional figure.
Formulas
Term/Concept / Description*Circle, Area / A = r2
*Circle, Circumference /
*Distance Formula / The distance between any two points with coordinates (x1,y1) and (x2,y2) is given by the formula
*Midpoint Formula / On a number line, the coordinate of the midpoint of a segment whose end points have coordinates a and b is .
In a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x1,y1) and (x2,y2) are
Rectangle, Area and Perimeter / P = 2l + 2w, A = lw
Square, Area and Perimeter / P = 4s, A = s2
Triangle, Area and Perimeter / P = a+ b + c, A = ½ bh
Postulates
Postulate*Ruler Postulate(1) / The points on any line can be paired with real numbers so that, given any two points P and Q on the line, P corresponds to zero, and Q corresponds to a positive number. The distance between the points is the absolute value of their difference.
Segment Addition Postulate(2) / If Q is between P and R, then PQ + QR = PR. If PQ + QR = PR, then Q is between P and R.
Protractor Postulate(3) / Given and some number n between 1 and 180, there exists one and only one ray with endpoint A that extends on either side of , such that the measure of the angle formed is n.
Angle Addition Postulate(4) / Given R is in the interior of PQS, then mPQR + RQS = PQS. If PQR + RQS = PQS, then R is in the interior of PQS.
Theorems
TheoremsMidpoint Theorem / If M is the midpoint of , then .
Pythagorean Theorem / In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.