Download CHAPTER ONE: Tools of Geometry Page 1 of 12

CHAPTER ONE: Tools of Geometry
Page 1 of 12
(1-1) Nets and Drawings for Visualizing Geometry
Given a standard six-sided die, what would it look like if I flattened it?
What about this solid?
... or this one?
A __________________ is a two-dimensional diagram that you can fold to form a three-dimensional figure.
A net shows __________________ of the surfaces of a figure in one view.
(1-2) Points, Lines, and Planes
undefined term = a term whose meaning is accepted _____________________________ a definition
Our undefined terms: _______________ , _______________, & _______________
CHAPTER ONE: Tools of Geometry
Page 2 of 12
Naming Them:
_________________________ is the set of all points in three dimensions.
A SEGMENT (or line segment) is part of a line that consists of _________________________ and
_______________ of the points in between them.
A _______________ is part of a line that consists of one endpoint and all of the points of the line
on one side of the endpoint.
_________________________ are two rays that share an endpoint and form a _______________.
CHAPTER ONE: Tools of Geometry
Page 3 of 12
A _________________________ or _________________________ is an accepted statement of fact.
Postulate 1-1: Through any two points there is _____________________________________.
Postulate 1-2: If two distinct lines intersect,
then they intersect in _____________________________________.
Postulate 1-3: If two distinct planes intersect,
then they intersect in ____________________________________.
Postulate 1-4: Through any three non-collinear points,
there is ____________________________________________ .
(1-3) Measuring Segments
Postulate 1-6 (Segment Addition Postulate):
If three points A,B, and C are collinear and B is between A and C, then ___________________________
Distance (on a number line):
Given two points A and B on a number line, the distance between them, d, is ______________________
The distance between A and B can also be written as ____________
CHAPTER ONE: Tools of Geometry
Page 4 of 12
Given a number line where…
G = ____________and J = ____________, find GJ.
P = ____________ and Q = ____________, find PQ.
Given EG where EF = ____________ and FG = ____________.
If EG = 59, find x, EF, FG, and EG
Equality vs Congruence:
Two objects are ______________________if they have the same ______________________.
Two objects are ______________________if they are the same ______________________.
Equal Segments vs Congruent Segments
Equality: _______________________
Congruence: _______________________
CHAPTER ONE: Tools of Geometry
Page 5 of 12
The ______________________of a segment is the point that divides the segment into two congruent segments.
The point, line, ray, or other segment that intersects
a given segment at its midpoint is a ______________________for that segment.
BE CAREFUL HERE! The midpoint is a ________________, while a bisector ____________________ the midpoint.
Q is the midpoint of PR. If PQ = ____________ and QR = ____________,
find x, PQ, QR, and PR.
(1-4) Measuring Angles
An ___________________ is formed by two rays with the same endpoint.
The rays are the ___________________ of the angle,
and the endpoint is the ___________________ of the angle.
SIDES: ___________ and ___________
VERTEX: ___________
CHAPTER ONE: Tools of Geometry
Page 6 of 12
Naming Angles:
1 => ___________
2 => ___________
___________
___________
___________
3 => ___________
___________
The ______________________________ of an angle is the region
containing all the points between the two sides of the angle; the ______________________________ of
an angle is the region containing all of the points outside of the angle.
Types of Angles:
___________________ angles measure between 0 & 90 degrees.
___________________ angles measure 90 degrees.
___________________ angles measure between 90 & 180 degrees.
___________________ angles measure 180 degrees.
Equal Angles vs Congruent Angles
Equality: _______________________
Congruence: _______________________
CHAPTER ONE: Tools of Geometry
Page 7 of 12
Postulate 1-8 (Angle Addition Postulate):
If point B is in the interior of AOC,
then ________________________________________
DEF is a straight angle.
Find m DEC and m CEF.
(1-5) Exploring Angle Pairs
______________________________ angles are
two coplanar angles with a common side,
a common vertex, and no other points in common.
______________________________ angles are two angles whose sides are opposite rays.
A little easier...
Vertical Angles are formed when __________________________________________________ intersect.
CHAPTER ONE: Tools of Geometry
Page 8 of 12
______________________________ angles are two angles whose measures have a sum of 90 degrees.
Each angle is called the ______________________________ of the other.
______________________________ angles are two angles whose measures have a sum of 180 degrees.
Each angle is called the ______________________________ of the other.
A _____________________________________________ is a pair of adjacent angles whose noncommon
sides are opposite rays. The angles of a linear pair form a straight angle.
Postulate 1-9 (Linear Pair Postulate):
If two angles form a linear pair, then they are _________________________________________.
An _____________________________________________ is a ray or segment that divides an angle
into two congruent angles.
CHAPTER ONE: Tools of Geometry
Page 9 of 12
XP bisects MXE. If m PXM = ___________, find m PXE and m EXM.
(1-6) Basic Constructions – moved to Chapter 2
(1-7) Midpoint and Distance in the Coordinate Plane
On a NUMBER LINE, the coordinate of the midpoint is the _______________ of the coordinates of the endpoints.
Given points A and B on a number line,
the midpoint M of AB is M =
On the COORDINATE PLANE,
the x-coordinate of the midpoint is the ______________________ of the x-coordinates
and the y-coordinate of the midpoint is the _____________________of the y-coordinates.
Given two points on the coordinate plane,
A(x1, y1) and B(x2, y2), the midpoint M of AB is M =
Given P = ___________ and Q = ___________;
find M, the midpoint of PQ.
CHAPTER ONE: Tools of Geometry
Given F = ___________ and G = ___________ ;
find M, the midpoint of FG.
Given AB with midpoint M. If A = ___________ and M = ___________,
find B, the OTHER ENDPOINT.
DISTANCE FORMULA:
The distance between two points, A(x1, y1) and B(x2, y2), is d =
If L = ___________ and M = ___________, find LM.
If S = ___________ and T = ___________, find ST.
Page 10 of 12
CHAPTER ONE: Tools of Geometry
Page 11 of 12
(1-8) Perimeter, Circumference, and Area
The ___________________________________ of a polygon is the sum of the lengths of its sides.
The ____________________________ of a polygon is the number of square units that it encloses.
For a SQUARE:
perimeter = ___________
area = ___________
For a RECTANGLE:
perimeter = ___________
area = ___________
For a TRIANGLE:
perimeter = ___________
area = ___________
CHAPTER ONE: Tools of Geometry
For a CIRCLE:
Page 12 of 12
perimeter ( ___________________________________ ) = ___________
area =___________
Postulate 1-10 (Area Addition Postulate): The area of a region is the ___________ of its non-overlapping parts.
Find the area of the pictured shape:
Find the area of the shaded region