Download Chapter 1 Honors Notes 1.2 Points, Lines, and Planes Objective: I

Chapter 1 Honors Notes
1.2 Points, Lines, and Planes
Objective: I can understand basic terms and postulates of geometry.
Term Description
How to Name It
A ______________ indicates
a location and has no size.
You can represent a point by
a dot and name it by a capital
letter such as A.
A ______ is represented by a
straight path that extends in
two directions without end.
A ____________________ is
represented by a flat surface
that extends without end.
Diagram
You can name a line by any
two points on the line or by a
single lower case letter that
is written at the end of the
line.
You can name a plane by a
capital letter or at least three
points in the plane that are
not all on the same line.
___________________________________________________ - points that lie on the same line
__________________________________________ - points and lines that lie on the same plane
Naming Points, Lines, And Planes
1.) What are two other ways to name line AD?
2.) What are two other ways to name Plane P?
3.) Name three collinear points.
4.) Name four coplanar points.
Definition
A ______________________
is part of a line that consists
of two endpoints and all the
points between.
How To Name It
Diagram
You can name a segment by
its two endpoints.
A _________________ is part
of a line that consists of one
endpoint and all the points
on one side of the endpoint.
You can name a ray by its
endpoint and another point
on the ray. The order of
points indicates the ray’s
direction. (ORDER MATTERS!)
_____________ are two rays You can name opposite rays
that share the same endpoint by their common endpoint
extend in opposite
and any other point on each
directions.
ray.
___________________________________________ - a rule that is accepted without proving it
Postulate 1-1: Through any two points there is exactly one distinct _______________________.
Postulate 1-2: If two lines intersect, then they intersect in exactly one ____________________.
Postulate 1-3: If two planes intersect, then they intersect in exactly ______________________.
Postulate 1-4: Through any three noncollinear points there is exactly _____________________.
Use the Diagram to Answer the Questions Below
5.) Name three segments.
6.) Name three rays.
7.) Name a pair of opposite rays.
8.) Name the intersection of Plane ABC and Plane BCD.
1.3 Measuring Segments/1.4 Measuring Angles
Objective: I can find and compare length of segments and measures of angles.
Postulate 1-5 Ruler Postulate: Every point on a line can be paired with a real number known as
a coordinate.
Postulate 1-6 Segment Addition Postulate: If three points A, B, and C are collinear and B is
between A and C, then __________________________________________________________.
1.) If PR = 25, PQ = 2x + 1, and QR = 3x + 4, then find QR.
2.) Find LN if M is between L and N, LN = 8x + 2, LM = 2x + 4, and MN = 3x + 19.
___________________________________________________ - segments with the same length
________________________________ - point dividing a segment into two congruent segments
______________ - a segment, ray, line, or plane that passes through the midpoint of a segment
3.) AB bisects CD at E. Find the value of x.
Naming and Classifying Angles
_______________
_______________
________________
__________________
___________________________________________________ - angles with the same measure
Postulate 1-8 Angle Addition Postulate: If B is in the interior of Angle AOC, then mAOB +
mBOC = mAOC.
Diagram:
4.) If the measure of angle ABD = 53, then find the value of x.
5.) AB and AC are opposite rays. If D is not on either line and the mBAD = 2x + 5 and
mDAC = 8x, find mDAC.
1.5 Exploring Angle Pairs
Objective: I can identify special angle pairs and use their relationships to find angle measures.
Definition
Example/Diagram
_______________________ are two coplanar
angles that share a side and a vertex. They
also have no common interior points.
__________________________________ are
two angles whose sides form opposite rays.
_____________________________________
are two angles whose sum is 90 degrees.
_____________________________________
are two angles whose sum is 180 degrees.
_____________________________________
are a pair of adjacent angles whose noncommon sides form opposite rays.
___________________________ is a ray that
divides an angle into two congruent angles.
Postulate 1-9 Linear Pair Postulate: If two angles form a linear pair, then
_____________________________________________________________________________.
Diagram:
Use the Diagram Below.
1.) Name two pairs of vertical angles.
2.) Name two pairs of adjacent angles.
3.) Name a linear pair.
4.) If Angle ABD and angle CBD are complementary, then the measure of angle CBD = ___?
5.) QS bisects angle PQR. Find the value of x.
6.) Angle PQS and SQR form a linear pair. Find the measure of angle PQS.
1.7 Midpoint and Distance Formula
Objective: I can find the midpoint of a segment and find the distance between two points in the
coordinate plane.
Description
On the Number Line
The coordinate of the
midpoint is the average of
the two coordinates of the
endpoints.
In the Coordinate Plane
The coordinates of the
midpoint are the average of
the x-coordinates and the ycoordinates of the endpoints.
Formula
Diagram
The coordinates of the
𝑎+𝑏
midpoint M of AB is 2 .
Given AB where A (x1, y1) and
B(x2, y2), the coordinates of
the midpoint of AB are
 x  x y  y2 
M 1 2 , 1

2 
 2
1.) Find the midpoint of A(2,5) and B(3,-15).
2.) The midpoint of AB is M(-2,1). One endpoint is B(-5,7). What are the coordinates of
the other endpoint A?
Distance Formula: The distance between two points A (x1, y1) and B(x2, y2) is d =
√(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2.
3.) Find the distance between P(-6,3) and Q(5,7).
Partitioning a Line Segment
4.) On a number line, A is at -2 and B is at 4. What is the location of C between A and B,
2
such that AC is 3 the length of AB? (draw the situation!)
5.) Points A(-2,-3) and B(8,2) are the endpoints of AB. What are the coordinates of point C
2
on AB such that AC is 5 the length of AB?