Geomerty Chapter 4 Flashcards
Betweenness
B is between A and C if (1) A, B and C are different point of the same line, and (2) AB + BC = AC. When B is between A and C, we write A-B-C or C-B-A.
Segment Bisector
The midpoint of a segment is aid to bisect the segment. The midpoint of a segment AB__, or any line, plane, ray, or segment which contains the midpoint and does not contain AB__, is called a bisector of AB__.
Angle
If two rays have the same end points but do not lie on the same line, then their union is an angle. The two rays are called its sides, and their common end point is called its vertex. If the rays are AB—> and AC—>, then the angle is denoted by <BAC or <CAB.
Interior and exterior of an angle
The interior of <BAC is the set of all points P in the plane of <BAC such that (1) P and B are on the same side of AC<—>, and (2) P and C are on the same side of AB<—>. The exterior of <BAC is the set of all points of the plane of <BAC that lie neither on the angle nor in its interior.
Triangle
If A, B, and C are any three non collinear points, then the union of the segments AB__, AC__, and BC__ is called a triangle, and is denoted by ∆ABC. (Important part)
The points A, B, and C are called its vertices, and the segments AB__, AC__, and BC__ are called its sides. Every triangle ∆ABC determines three angles, namely, <BAC, <ABC, and <ACB. These are called the angles of ∆ABC. The perimeter of a triangle is the sum of the lengths of its sides.
Interior and Exterior of a triangle
A point lies in the interior of a triangle if it lies in the interior of each of the angles of the triangle. A point lies in the exterior of a triangle if it lies in the plane of the triangle but does not lie on the triangle or in the interior.
Interior—in each angle
Exterior—not in the triangle or interior
State Postulate 11
Angle Measurement Postulate
To every angle <BAC there corresponds a real number between 0 and 180.
Definition of The Angle Measurement Postulate
The number given by the Angle Measurement Postulate is called the measure of <BAC, and is written m<BAC.
State Postulate 13
The Angle Addition Postulate
If D is the interior of <BAC, then
m<BAC = m<BAD + m<DAC.
Linear Pair definition
If AB—> and AD—> are opposite rays, and AC—> is any other ray, then <BAC and <CAD form a linear pair
Linear Pair definition
If AB—> and AD—> are opposite rays, and AC—> is any other ray, then <BAC and <CAD form a linear pair.
Supplementary definition
If the sum of the measures of two angles is 180, then the angles are called supplementary, and each is called a supplement of the other.
State Postulate 14
The Supplement Postulate
If two angles form a linear pair, then they are supplementary
State Postulate 14
The Supplement Postulate
If two angles form a linear pair, then they are supplementary
Right Angle, Obtuse, and Acute definition
A right angle is an angle having measure 90. An angle with measure less than 90 is called acute. An angle with measure greater than 90 is called obtuse.
