Susan Chaffee
Geometry Chapter 1
Spring 2009
Lesson 2 – Sections 1.3-1.4
Unit: Chapter 1 Tools of Geometry
Lesson: Section 1.3
Section 1.4
Points, Lines, and Planes
Segments, Rays, Parallel Lines, & Planes
Lesson Goals: The student will understand the building blocks of Geometry, including the 1st 4
postulates. The properties of segments, rays, and lines will be introduced.
Enduring Understanding:
Essential Questions:
 How are lines, points, and planes defined? What are the postulates?
Materials and/or Special Notes:
 Anticipation guide for video.
 Worksheets 1.3 and 1.4
 Block or box for demonstrating parallel lines
 Index cards for students to use a manipulative in intersecting planes
Anticipation Guide, before video.
Go over the Anticipation guide and ask students what their answers were.
Geometry video, part 2 (only show part of video section 1-3 (5:55-4:00) and section 1-4(1:50-0:00))
Go over the Anticipation guide and ask students if they changed any answers.
Section 1-3 Points, Lines, and Planes.
History: Euclid’s Elements. 300 B.C., 1st mathematician to formally write down geometric properties.
His works still hold true today. The point, line, and plane are the basic terms that are used to represent
Euclidean Geometry.
Work through anticipation guide as we define these.
Study tip: Use (Defn) and highlight
(Def) Point – a location, has no size
Notation: usually use a single capital letter to represent.
(Def) Line – infinite number of points extending in two opposite directions (no distance in defn)
Notation: ⃡𝐴𝐵 , emphasize the double arrow
Example: 𝑚 or ⃡𝐴𝐵, ask for suggestions of other names
(Def) Collinear – points lying on the same line
Example: A and B are collinear
NonExample: A. B, and C are not collinear
Susan Chaffee
Geometry Chapter 1
Spring 2009
(Def) Plane – a flat surface, extending infinitely in direction of all lines contained in the plane
Notation: Name with 3 or more (noncollinear) points. Plane ABCD is a plane containing
points A,B,C,D , or Plane ABD, or a single letter is sometimes used when the letter is NOT a
point.
Handout worksheet Practice 1-3
WS #1-3, #22,#23
(Def) Coplanar –lying on the same plane
Example: ABC are coplanar
NonExample: A, B, C, and D are not coplanar.
Box demo. – show planar and coplanar with a box. Show how 2 points on one side and a line on
another plane wouldn’t be coplanar.
History: Euclid’s geometry is defined by a set of rules that are accepted without proof (physically
“obvious”), known as Euclid’s postulates. P.794 of text lists all of them.
(next to Bible, most read book of all time!)
Postulate (axiom) – statement accepted without proof (physically obvious, but not able to prove)
Theorem – can be proved using the axioms (Pythagorean Thm is an example)
Postulate 1-1: Two distinct points determine a line
Example: Line m is the only line passing through the two points.
What this says -> Given any 2 points, we can put a line between them!
2 points are always collinear, 3 points might not be.
Postulate 1-2: If 2 lines intersect, then they intersect in exactly one point
Example: Recall system of 2 linear equations
Look at the wall and floor, think of these as 2 planes, what does the intersection look like?
Postulate 1-3: If two planes intersect, then they intersect in exactly one line.
Postulate 1-4: Three noncollinear points determine exactly one plane.
What this says -> Given any 3 points, we can lie a plane on them.
3 points are always coplanar, 4 points might not be.
Ask if students know what a tripod is. Why is a tripod 3 legged and not 4? (think about a 4 legged table,
why does it wobble?)
Worksheet 1.3 index cards, #4-15,17-20, 24, 25, 26, 30,31
Susan Chaffee
Geometry Chapter 1
Spring 2009
Section 1-4 Segments, Rays, Parallel Lines, and Planes
Finish video (1:50-0:00). Recall Line, extends infinitely in both direction.
(Def) Segment – Part of line, consisting of two endpoints and all points between them.
Notation: ̅̅̅̅
𝐴𝐵 and example
Q: How are a line and segment different?
(Def) Ray – part of line consisting of one endpoint and all points on one side of the line
Notation: 𝐴𝐵, where A is the endpoint and the points extend infinitely in direction of B (could be
any point on that side)
Example: Sunbeam, needs a starting point.
Q: Are 𝐿𝑃 and 𝑃𝐿 the same ray?
(Def) Opposite rays – Two collinear (on same line) rays with same endpoint, in opposite directions
Example: 𝐴𝐵 and 𝐴𝐶 are opposite rays and always form a line.
NonExample: 𝐴𝐵 and 𝐵𝐴 are NOT opposite rays
WS1.4 #1-4 (me) #14-19 (individual)
Block for demonstration
(Def) Parallel Lines – Lines (or segments) lying in the same plane that do not intersect.
⃡ and 𝐸𝐹
⃡ ∥ 𝐸𝐹
⃡ are parallel and write this as 𝐴𝐵
⃡ .
Notation: We say lines 𝐴𝐵
⃡ ∥ 𝐸𝐹
⃡
Example: 𝐴𝐵
⃡ ∦ 𝐸𝐹
⃡ , (not parallel lines)
NonExample: 𝐶𝐷
Skew Lines – lines that are noncoplanar, (which implies they are not parallel and do not intersect)
Example: See box. Note: If lines are in the same plane they either intersect or are parallel.
WS1.3 #28
Parallel Planes – Planes that do not intersect.
Notation: 𝑃𝑙𝑎𝑛𝑒 𝐴𝐵𝐶𝐷 ∥ 𝑃𝑙𝑎𝑛𝑒 𝐺𝐻𝐼𝐽
Hints: Trace with your finger, where do you cross twice? This is the intersection.
WS1.4 #7-13
Text: Algebra 1 Review
Lesson Closure: Notation is important! Put list of notation on board and have students identify if it is a
line, ray, or segment, and number of endpoints for each.
Assignments: p.19, #1-24,30-32,35-41, p.25, #1-4,6,8,10-19,25,28,29, p.30,#3,9,14,17,18
Assessment:
 Formative: Anticipation guide before/after video
 Summative: Informal quiz tomorrow over (use clicker perhaps). P.21, #55- 60,p.26 #25-33.