Transcript 1.1 Building Blocks of Geometry

Good Morning
Lesson 1.1
Building Blocks of Geometry
Homework:
Geometry - Lesson 1.1/ 1-31 odds
Quiz Friday – Lesson 1.1
Basic Geometric Figures
• Undefined terms:
♥Line
♥Point
♥Plane
Point
• Points have NO size and are often shown
as dots.
HOW TO WRITE:
♥ Points are named as ONE capital letter
such as A or X
.A
Lines
• A line has no thickness, but has infinite
length. It is an straight arrangement of an
infinite amount of points.
.
Y
.
X
HOW TO WRITE:
♥ Lines are named by two points (capital
letters) on the line, topped with miniature
version of a line on top.
Or
m
♥ a single lowercase script letter.
line m
Plane
• A plane has length and width, but no height. It
extends infinitely in all directions along a flat
surface.
HOW TO WRITE:
♥ A plane can be named by three points
(THREE capital letters) that lie in the plane.
.
A
.
.
Plane ABC
C
B
Or
♥ It can be named by one script capital letter
such as R.
Plane R
R
Collinear
♥ Points on the same line, together.
.
.
Z
Y
.
X
Points X, Y, & Z
are collinear
Coplanar
♥ Points, lines, …, on the same plane,
together
.
A
.
.
B
C
Segment
• A segment is a part of a line that begins at
one point and ends at another. The
points are called the endpoints of the
segment.
G
H
♥ HOW TO WRITE:
– The endpoints are capital letters and have a
bar over them.
Ray
♥ A ray is a part of a line that starts at a
point and goes infinitely in one direction.
Q
P
♥ The point is called the endpoint of the ray
P
Q
♥ HOW TO WRITE: Two capital letters with
a ray on top. Be sure to have the endpoint
above the endpoint letter!
Angle
♥ An angle is formed by two rays with a common endpoint.
♥ The endpoint is called the vertex of the angle and the
rays are the sides of the angle.
♥ An angle divides a plane into two regions: the interior
and the exterior.
Angles
♥ HOW TO NAME IT: Use THREE capital
letters with the vertex in the middle and
the angle sign in front. The three letters need to
be in the order that they would be if you traced the angle
with your finger.
D
F
E
OR
By the angle sign and the vertex ONLY IF
there is only one angle at the vertex.
Multiple angles with a shared
vertex
A
B
D
C
E
There are 4 angles with vertex B, therefore
each angle MUST be named using 3 points
specific to that angle.
Midpoint
• Midpoint of a segment is the point on the
segment that is the same distance from both
endpoints
– bisects the segment
– divides the segment into two congruent segments
• Congruent markings on a segment indicate a
point is a midpoint
Q
●
U
●
E
●
Congruent markings, aka, slash marks
Midpoint of WHAT?
• Can a point have a midpoint ?
– a line?
– a square?
– a plane?
– NO, only a segment is finite in length
– There is NO midpoint to infinity
Conjectures
A conjecture is a statement that is
accepted as true without proof.
In other words, a conjecture is so
obvious, and makes so much
sense, there is no need to prove it.
Our first 5 Conjectures
POINT
1. The intersection of two lines is a ________
LINE
2. The intersection of two planes is a ______.
3. Through any two points there is exactly one
LINE
_______.
4. Through any three noncollinear points there is
PLANE
exactly one ______.
5. If two points are in a plane, then the line
IS ALSO IN THE PLANE.
containing them ____________________.