Geometry
Geometry Name_____________________________
CH 1 Study Guide Date__________________
VOCABULARY
|point line plane angle |
|collinear points line segment ray sides |
|opposite rays intersect linear pair vertex |
|midpoint formula angle bisector acute angle bisect |
|segment addition postulate collinear plane midpoint vertical angle |
|supplementary angles distance formula obtuse angle congruent angle |
|complementary angles congruent segments right angle straight angle |
|angle addition postulate adjacent angles segment bisector |
1.2 Points, Lines, Planes
Point – represents a location, no size, no thickness .A
Line – infinite set of points, no thickness, extends in both directions forever (straight line)
Name - line m, [pic]
Plane – Flat surface that extends forever, made up of infinite points and lines
Must be 3 points not in a line
Plane M, Plane ABC
Collinear Points – all points that lie on the same line
Collinear Plane – all points that lie on the same plane
Line Segment – Consists of 2 endpoints and all the points between them
[pic]
Ray – The ray AB consists of the initial point A and all the points that lie on the same side of A as point B
Opposite Rays –– 2 rays that share exactly 1 point. If C is between A and B, then [pic] are opposite rays.
Intersect – 2 or more geometric figures intersect if they have 1 or more points in common.
Intersecting Planes Line Interesting Plane
2 planes intersect in a line.
1.3 Segments and Their Measures
Distance/Length – same meaning
[pic] = line segment AB
AB = refers to the length of segment AB
[pic] = line AB
[pic] = ray AB
Between refers to collinear points. When 3 points lie on a line, you can say that one of them is between the other two.
Distance Formula
AB = [pic]
Find the length of the segments.
AB = [pic]
[pic]
[pic]
[pic]
Congruent Segments – segments that have the same length
[pic] [pic] (is congruent to)
Segment Addition Postulate – If B is between A and C then AB + BC =AC
1.4 Angles and Their Measures
Angle – 2 different rays that have the same initial point
Sides – the rays that make up the angle. [pic]
Vertex – the initial point of the angle
Name – [pic]
Measure = [pic]
Congruent angles – angles that have the same measures
A point is in the interior of an angle if it is between points that lie on each side of the angle.
A point is in the exterior of an angle if it is not on the angle or in its interior.
Angle Addition Postulate – If P is in the interior of [pic]
Acute angle – an angle with measure between 0 and 90
Right angle – an angle with measure equal to 90
Obtuse angle – an angle with measure between 90 and 180
Straight angle – an angle with measure equal to 180
[pic]
Adjacent angles – 2 angles that share a common vertex and side, but have no common interior points
[pic]are adjacent angles
1.5 Segment and Angle Bisectors
Midpoint – the point that divides segment into two congruent segments.
Bisect – to divide into 2 congruent parts
Segment bisector – a segment, ray, line, or plane that intersects a segment at its midpoint
Midpoint Formula – If A(x ,y ) and B(x ,y ) endpoints of a segment then the midpoint of AB is
[pic]
Find the coordinates of the midpoint of AB with A(-2,3) and B(5,-2)
Angle Bisector – a ray that divides an angle into 2 adjacent angles that are congruent.
1.6 Angle Pair Relationships
Vertical Angles – 2 angles whose sides form 2 pairs of opposite rays
[pic]
Linear Pair – 2 adjacent angles whose non common sides are opposite rays
[pic]
Complementary Angles – 2 angles whose measures have the sum 90
Complementary adjacent Complementary nonadjacent
Supplementary Angles – 2 angles whose measures have the sum 180
Supplementary adjacent Supplementary nonadjacent
1.7 Introduction to Perimeter, Circumference, and Area
Formulas
Square
P = 4s
[pic]
Rectangle
Length l and width w
P = 2l + 2w
Triangle
Side lengths a, b, and c, base b, and height h
P = a+b+c
[pic]
Circle
Radius r
[pic]
[pic]
-----------------------
A
B
C
D
m
A
B
C
B
A
A
B
C
20
120
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