Basic High School Geometry Book
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chap 1
1) It may be hard for some to use inductive reasoning because it involves using logic. For example, when there is a sequence of numbers, where a number equals 2, the next number equals 4, and the next 6, the next number is supposed to be assumed to be 8 because it is observed that each number is added by 2 to get the next number. 8 would be the conjecture
. 2, (+2) 4, (+2) 6, ...(+2 =?)... 8
2) To understand points and lines, think of stars. Each star is a point on a plane ( the sky ). Space, the set of all points, would be the part of the sky you can see containing all the stars you can see. If you connected two stars and the straight line created would never end, it is in fact a line. A line can be named by any two points on the line with a line on top with two arrows pointing each way ($) or by a single lowercase letter. A point is normally represented by a small dot and named by a capital letter, and a plane can be named by either a single capital letter or by at least three noncollinear points. If that line passed through a third star, the three stars would be considered collinear. All the lines are points in the sky, on the same plane, are coplanar.
To understand intersecting planes, the sky must not be in mind. Instead, picture a plane as being a sheet of paper, just keep in mind that a plane extends in all directions infinitely. If to sheets of paper (plane A and plane B) were put into an x-type position, a line (line CB) is the intersection. A plane cannot be represented by three collinear points because there are an infinite number of planes that could that contain the points
3) Some lines may not be infinite, but they have different names. A segment is a part of a line consisting of two endpoints. There is no infinite in a segment because it ends at its endpoints. A ray, on the other hand, has only one endpoint, therefore continues infinitely in the other direction. A segment is named by its two endpoints with a line ( G) on top of them. A ray is named by its endpoint and any other point on the ray with a ray symbol on top ( 6). Two rays with the same endpoint pointing in opposite directions are called opposite rays.
If two lines never intersect they are parallel ( 2). Parallel lines never intersect because their slopes are identical, and they are always the same distance apart in both directions. Skew lines do not lie in the same plane as seen below. They never intersect and are not parallel. Parallel planes never intersect just as parallel lines.
line l 2 line g line t and line l are skew
4) Any two segments with the same length are congruent ( -). An angle (p) is formed by two rays ( called sides of the angle) with the same endpoint ( called the vertex). You can name an angle several ways: by the vertex (which is a point so it’s represented by a capital letter pB), a number located inside the angle by the vertex ( p1), or by a point on each line and the vertex with the vertex always in the middle ( pABC). You can classify angles according to their measures. If an angle is less than 90o, it is acute. If an angle is equal to 90o, it is right. A right angle is represented by a symbol (5) over the vertex. If an angle is greater than 90o but less than 180o, it is obtuse. If an angle is equal to 180o, it is straight. The angles on each side of a straight angle are congruent. Angles with the same measure are also congruent.
5) Perpendicular lines are two lines that intersect to form right angles. The symbol z is used to represent the phrase “is perpendicular to.” A perpendicular line is the complete opposite of a parallel line. The perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to a segment at its midpoint. An angle bisector is a ray that divides an angle into two congruent angles.
6) Vertical angles are two angles whose sides are opposite rays. If two lines intersect the top and bottom angles would be vertical angles and the side angles would be vertical angles. Adjacent angles are just what they are called, adjacent. Adjacent angles share a side and a vertex. Complementary angles have angles whose sum equals 90o; therefore, when two complementary angles are adjacent they make a right angle. Supplementary angles have a sum of 180o and form a straight angle when adjacent.
p1 & p4 are vertical angles
p1 & p2 are complementary angles
p4 & p5 are supplementary angles
7) In coordinate geometry you can describe a point with an ordered pair (x,y). To graph a point first find the x-value (x,y) along the horizontal x-axis, then follow up until the point is also even with the y-value (x,y) along the vertical y-axis. The point should be above or below the x-value and left or right the y-value. A line can be graphed by the equation y= mx + b. m is the slope of the line found by rise over run. b is the y-intercept. Follow the y-axis to find the y-intercept and make it a point. Move up and over the amount given by the slope to make another point. Use the two points to make a line.
Distance is the amount of units between two points. The shortest distance is a straight line from one point to the other. It is easy to find if the two points lie on a horizontal or vertical lines, just subtract. If they do not, it can be found with the distance formula . Midpoint is a point that divides a segment into two congruent segments and can be found by using the midpoint formula [ 2M = (x1 + x2, y1 + y2)]
D=
distance formula