Geometry
CH 1 Study Guide
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Date__________________
VOCABULARY
point
collinear points
opposite rays
midpoint formula
segment addition postulate
supplementary angles
complementary angles
angle addition postulate
line
line segment
intersect
angle bisector
collinear plane
distance formula
congruent segments
adjacent angles
plane
angle
ray
sides
linear pair
vertex
acute angle
bisect
midpoint
vertical angle
obtuse angle
congruent angle
right angle
straight angle
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)
m
A
B
C D
Name - line m, AB AC CB
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
Ray – The ray AB consists of the initial point A and all the points that lie on the same
A
side of A as point B
B
Opposite Rays –– 2 rays that share exactly 1 point. If C is between A and B, then CA and CB are opposite
rays.
A
C
B
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
AB = line segment AB
AB = refers to the length of segment AB
AB = line AB
AB = 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 =
( x 2  x1 ) 2  ( y 2  y1 ) 2
Find the length of the segments.
(4  1)  (3  1)
(3)  (2)
94
13
2
AB =
2
2
Congruent Segments – segments that have the same length
AB  DC
 (is congruent to)
D
A
B
C
Segment Addition Postulate – If B is between A and C then AB + BC =AC
A
B
C
2
1.4 Angles and Their Measures
Angle – 2 different rays that have the same initial point
Sides – the rays that make up the angle. AC AB
Vertex – the initial point of the angle
Name – A CAB BAC 1
Measure = mCAB  40
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
RST then mRSP  mPST  mRST
Acute angle – an angle with measure between 0 and 90
20
Right angle – an angle with measure equal to 90
Obtuse angle – an angle with measure between 90 and 180
120
Straight angle – an angle with measure equal to 180
Adjacent angles – 2 angles that share a common vertex and side, but have no common interior points
LMN and NMO 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
midpoint
intersects a segment at its
Midpoint Formula – If A(x ,y ) and B(x ,y ) endpoints of a segment then the midpoint of AB is
x1  x2 y1  y 2
,
2
2
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
Linear Pair – 2 adjacent angles whose non common sides are opposite rays
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
A  s2
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
1
A  bh
2
Circle
Radius r
C  2r or
A  r 2
C  d