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Unit Title:
Building Blocks of Geometric Figures: Line Segments and Angles
Subject/Topic Areas
Key Words
Point
 Definitions of basic geometric terms.
Collinear
 Undefined terms.
Coplanar
 Using postulates and formulas to find
Parallel
lengths of segments and measures of
Perpendicular
angles.
Skew
 Naming angles and line segments.
Plane
Line
Line Segment
Ray
Angle
Congruent
Measure
Angle Addition Postulate
Segment Addition Postulate
Distance Formula
Mid-point Formula
Equidistant
Perpendicular Bisector
Grade Level
Book
Chapter/Pages
Length of Unit
9-12
Prentice Hall California
3 weeks
Geometry
California Standards contained in the Unit:
1. Students demonstrate understanding by identifying and giving
examples of undefined terms, axioms, theorems, and inductive
and deductive reasoning.
1.1. Students can identify undefined terms.
1.2. Students can give examples of undefined terms.
1.3. Students can identify axioms.
1.4. Students can give examples of axioms.
1.5. Students can identify theorems.
1.6. Students can give examples of theorems.
1.7. Students can identify inductive reasoning.
1.8. Students can give examples of inductive reasoning.
1.9. Students can identify deductive reasoning.
1.10. Students can give examples of deductive reasoning.
17. Students prove theorems by using coordinate geometry,
including the midpoint of a line segment, the distance formula,
and various forms of equations of lines and circles.
17.1. Students use the midpoint formula to prove theorems.
17.2. Students use the distance formula to prove theorems.
17.3. Students use equations of lines to prove theorems.
17.4. Students use equations of circles to prove theorems.
Brief Description of the Unit:
Students will learn basic vocabulary needed to communicate about Geometry, how to express problems
using mathematical symbols, and how to perform mathematical operations on geometric figures.
Stage 1: Unit Goals
What essential and unit questions will drive the focus this unit (Essential Questions)?
1. Why is it important to have a common language and rules for how to do things?
 What might happen if we did not agree on and follow conventions for naming angles and line
segments?
 Why are there different words to express that two things are the same as each other? How do
we know when to use each?
2. Which mathematical operations can be used on things other than numbers?
 What does addition look like with Geometric figures?
 What does division look like with Geometric figures?
 What does subtraction look like with Geometric figures?
 What does multiplication look like with Geometric figures? (not relevant in this unit but leads
into area)
3. How do tools like maps and graphs help us explore the physical world?
 How can the distance formula help you?
 How can the midpoint formula help you?
What will students understand as a result of this unit (Big Ideas)?
The relationships between the parts and the whole that they compose, specifically regarding angles and
line segments and that they can be manipulated algebraically.
That length and distance are interrelated.
That there are different ways to describe a line- by length between points and by location of those
points.
Students will know… (List facts, concepts,
Students will be able to…
principles and generalizations)
(List skills, procedures, and strategies)
The segment addition postulate.
Name angles in two ways.
The angle addition postulate.
Name line segments.
Definitions of lines, rays, line segments, angle,
Solve problems using the distance formula.
congruence, points, and planes.
Find the midpoint of a line segment.
Construct a perpendicular bisector.
Add line segments.
Add angles.
Manipulate formulas for lines without numerical
values (using letters).
Stage 2: Acceptable Evidence
Performance Tasks, Projects, Problems
Find distance between two locations on a map.
Find the midpoint of those locations.
Find a point equidistant from those points.
Physical representation of intersecting lines and planes using manipulatives.
CST practice problems on length using letters instead of numbers as coordinates.
Academic Prompts
Quizzes and Tests
Summarize the relationships between distance,
length, midpoint, and bisectors.
In what ways can two lines intersect or not?
In what ways can two planes intersect or not?
In what ways can a line and plane intersect or not?
Other Evidence
Frayer Models for vocabulary.
Thinking Map to compare and contrast related
vocabulary.

Matching terms and pictures, fill-in-theblank quiz for vocabulary.
 Unit Test is a project that asks them to find
the lengths of the sides of polygons given
endpoints, consecutive segments, and
perpendicular bisectors.
Student Self-Assessment
Warm Ups at beginning of each class period.
Practice problem worksheets that are selfcorrected.
Practice Test.
Stage 3: Plan Learning Experiences and Instruction
Key teaching and learning experiences that will equip students to demonstrate the targeted
understanding?
Concept map about dimensionality.
Frayer Models for point, plane, line, ray, line segment, angle.
Worksheets to practice applying the addition postulates to plain models and in context.
Apply distance formula, midpoint formula, and perpendicular bisector to locations on a map.
Daily Lesson Plans
Activity and Description:
Duration Day
Warm Up: Quick Write about experience with Geometry. DO you know any
definitions?
Introduce unit and discuss prior knowledge about Geometry. Emphasize lines,
angles, figures, and solids. Explore examples of lines, figures, and solids to
brainstorm ideas for how to categorize them.
5
minutes
1
10
minutes
1
Concept Map: Dimensionality.
20
minutes
1
5
minutes
3
minutes
5
minutes
8-10
minutes
1
Describes the differences and similarities of
one, two, and three dimensional objects. Elaborate on the concepts and vocabulary
that apply to each.
Discuss concept maps. Which vocabulary belongs in each category? Can you have a
3D object without 1D or 2D object?
Add point as a non-dimensional term. Mention that we use points to name the
other objects.
Shade the 0D and 1D areas of the concept map as “undefined terms” and explain
that undefined terms are used to make definitions of the figures they compose.
Exit Ticket: On an index card, draw an example of one of the terms we discussed
and put the name on the back. Assign terms by row. Collect and use them as flash
1
1
1
cards to dismiss students.
Show them how to name lines and angles.
2
2
2
2
2
2