Geometry Chapter Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment


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1 Geometry Chapter 1 Section Term 1.1 Point (pt) Definition A location. It is drawn as a dot, and named with a capital letter. It has no shape or size. undefined term 1.1 Line A line is made up of points and has no thickness or width. It goes no forever (represented by arrows). You can name a line with ONLY TWO points on the line (with a line symbol above it) or with a lowercase script letter. **There is exactly one line through any two points. undefined term 1.1 Collinear (1.1) 1.1 Plane (pl.) (1.1) 1.1 Coplanar (1.1) 1.1 Space (1.1) Points that are on the same line are collinear. A flat surface made up of points. A plane has no depth, only length and width. It is drawn as a shaded foursided figure and named by any three noncollinear points or a uppercase script letter. undefined term **Through any three noncollinear points is exactly one plane. Points that exist on the same plane are coplanar. Space is a boundless, three dimensional set of all points. Space can contain lines and planes. In space, lines intersect at one point, and planes intersect at one line. Name 1.2 Line Segment (seg) 1.2 Measure of a Segment A line segment is part of a line with a beginning and end. The points that create the beginning and end are called endpoints. You name a segment by its endpoints and a segment symbol above them. Can be written in two ways: 1. the endpoint letter with no symbol the distance from point to point 2. a lowercase m in front of the name of the line segment with the segment symbol above it  the measure of segment
2 1.2 Precision Precision of any measurement depends on the smallest unit available. Your precision will be half of the smallest unit available. To find smallest unit, think of the increments you are counting or measuring by. (i.e. 48cm to 49cm to 50cm has a smallest increment of 1 cm, so the precision is 0.5 cm) 1.2 Betweenness of points A point is between two other points if you can add the smaller segments created with the point and it equals the bigger segment. If M is between A and B, then AM + MB = AB
3 1.2 Congruent Segments segs If two segments are equal in measure, then they are congruent. If two segments are congruent, then they are equal in measure. If =, then. If, then =. 1.3 Distance The distance between two points is the length of the segment connecting them and can be found with the distance formula: The distance between points x, y and x, y x x y y can be found by: Find CD if C(2, 6) and D(1, 3). 1.3 Midpoint (mp) A midpoint of a segment is the point halfway between the endpoints of a segment. If a point is a midpoint, then it divides the segment into two equal segments. If a point divides a segment into two equal segments, then it is the midpoint. The mp between points, and, x y x y can be found by x x, y y Find the mp of CD if C(1,2) and D(5, 3).
4 1.3 Segment Bisector (seg bis) Any segment, line, or plane that intersects a segment at its midpoint is called a segment bisector. If segment is bisected, then it s divided into two equal segments. If a segment is divided into two equal segments, then it is bisected. 1.4 Degree Unit of rotation around a circle. A unit for measuring angles. Symbol: 1.4 Ray A ray is part of a line. It has one endpoint and extends infinitely in one direction. Rays are named using the endpoint first (always) and one other point on the ray. You can only use the 1.4 Opposite Rays 1.4 Angle or two letters and the ray symbol above it. If you choose a point on a line, that point determines exactly two rays called opposite rays. Looks like a straight line An angle is formed by two rays that have a common endpoint. The rays are called the sides of the angle, and the common endpoint is called the vertex of the angle. 1.4 Right Angle If an angle measures 90 degrees, then it is a right angle. If an angle is a right angle, then it measures 90 degrees. 1.4 Acute Angle If an angle measures between 0 and 90 degrees, then it is an acute angle. If an angle is an acute angle, then it measures between 0 and 90 degrees. 1.4 Obtuse Angle If an angle measures between 90 and 180 degrees, then it is an obtuse angle. If an angle is an obtuse angle, then it Straight Angle measures between 90 and 180 degrees. If an angle measures 180 degrees, then it is a straight angle. If an angle is a straight angle, then it
5 1.4 Congruent Angles s measures 180 degrees. A straight angle looks like a straight line, but since we are looking at it in terms of rotation, it measures 180 degrees, it can be both an angle and a straight line. If two angles are equal in measure, then they are congruent. If two angles are congruent, then they are equal in measure. If =, then. If, then =. 1.4 Angle Bisector If a ray divides an angle into two congruent angles, then it is an angle bisector. If ray bisects an angle, then it divides it into two congruent angles.
6 1.5 Adjacent Angles Two angles that lie in the same plane, have a common vertex, common sides, BUT do NOT overlap. 1.5 Vertical Angles Two nonadjacent angles formed by two intersecting lines. 1.5 Linear Pair Pair of adjacent angles whose noncommon sides are opposite rays. 1.5 Complementar y Angles Comp 1.5 Supplementary Angles Supp 1.5 Perpendicular lines s s If two angles are complementary, then they add up to 90 degrees. If two angles add up to 90 degrees, then they are complementary. **They do not have to be adjacent to be complementary, but if they are adjacent they will form a right angle. If two angles are supplementary, then they add up to 180 degrees. If two angles add up to 180 degrees, then they are supplementary. **They do not have to be adjacent to be supplementary, but if they are adjacent they will form a straight angle and be a linear pair. If two lines are perpendicular, then they intersect to form 90 degree angles If two lines intersect to form 90 degree angles, then they are perpendicular.
7 1.5 Assumptions Be careful with diagrams, just because something looks like it is true does not mean that it is true. What you can assume from a diagram: 1. Adjacent angles 2. Linear pairs 3. Supplementary angles CANNOT ASSUME: 1. Right Angles 2. Perpendicular or parallel lines Congruent segments or angles 1.6 Polygons A closed figure whose sides are all segments that only intersect one other side at each endpoint. It is named by all of the endpoints (vertices) in consecutive order. 1.6 Concave Polygon 1.6 Convex Polygon 1.6 Classifying Polygons It is a polygon with at least one angle that is greater than 180 degrees. It looks dented or caved in. It is a polygon with all angles measuring less than 180 degrees. A polygon can be classified by the number of sides that it has. A polygon with n number of sides is called a ngon. Number of Polygon name sides (n) n
8 1.6 Regular Polygon A polygon that is equilateral (all sides are equal) and equiangular (all angles are equal). 1.6 Perimeter The perimeter of a polygon is the sum of the lengths of its sides. **To find the perimeter of a figure when given coordinates, requires you to use the distance formula for each side, then add those lengths (distances).
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