Grade/Course: Geometry (First Semester)
Instructional Unit 3: Proving Geometric Theorems
Instructional Schedule: First Nine Weeks (suggested for 18 days)
Adapted from Timothy Kanold Scope-and-Sequence documents
Standards:
Evidence Of Standard:
(student should be able to…)
Prerequisite Knowledge:
Assessment Tools:
(standards linked to content taught in
( formative assessments, quizzes,
previous grades)
mastery tasks/activities)
Prove geometric Theorems. (key content)
*Emphasis should be on the many roles of proof and a focus on the mathematical practice of making viable arguments and critiquing the reasoning of others.
(PASS 2.2a,2.2b,2.2c) Determine
- Verify lines are parallel using
unknown values and determine
relationships between corresponding
unknown values using the relationship
angles, alternate interior angles,
between:
alternate exterior angles, and same1. Angle addition and segment
side interior angles.
addition.
- Determine unknown values and
2. Complementary,
determine unknown values using the
supplementary, and vertical
relationship between:
angles.
 Angle addition and segment
Verify lines are parallel using
addition.
relationships between corresponding
 Complementary,
angles, alternate interior angles,
supplementary, and vertical
alternate exterior angles, and sameangles.
side interior angles.
(BA/PASS 2.2b) Prove theorems about
-Prove theorems about lines and
lines and angles. Theorems include:
angles using deductive reasoning
vertical angles are congruent; when a
(such as the law of syllogism).
transversal crosses parallel lines,
-Prove a theorem stating vertical
alternate interior angles are congruent angles are congruent.
and corresponding angles are
-Prove a theorem stating when a
congruent; points on a perpendicular
transversal crosses parallel lines,
bisector of a line segment are exactly
alternate interior angles are
those equidistant from the segment’s
congruent and corresponding angles
endpoints.
are congruent.
-Prove a theorem stating points on a
perpendicular bisector of a line
segment are exactly those
equidistance from the segment’s
endpoints.
Use coordinates to prove simple geometric theorems algebraically. (key content)
*This unit establishes Coordinate Geometry proof using both slope and the distance formula.
(BA/PASS 5.1) Prove the slope criteria
for parallel and perpendicular lines and
use them to solve geometric problems
(e.g., find the equation of a line parallel
or perpendicular to a given line that
passes through a given point or
determine if two lines are parallel,
perpendicular, or neither).
(BA/PASS 5.1) Use coordinates to
compute perimeters of polygons and
areas of triangles and rectangles, e.g.,
using the distance formula to find the
length of a segment.
(BA/PASS 5.2a) Use coordinates to
prove simple geometric theorems
algebraically through determining the
type of figure based on its properties.
For example, prove or disprove that a
figure defined by four given points in
the coordinate plane is a rectangle;
prove or disprove that the point (1, √3)
lies on the circle centered at the origin
and containing the point (0,2).
-Graph a line on the coordinate
plane.
-Translate a line parallel to another
line on the coordinate plane by
preserving its angle.
-Determine if two lines are parallel
by examining their slopes.
-Find the equation of a line parallel
or perpendicular to a given line that
passes through a given point.
-Rotate a line perpendicular to
another line on the coordinate
plane.
-Determine if two lines are
perpendicular by examining their
slopes.
-Prove the slope criteria for parallel
and perpendicular lines and use
them to solve geometric problems.
- Use coordinates to compute
perimeters of polygons and areas of
triangles and rectangles, e.g., using
the distance formula to find the
length of a segment.
-Identify the appropriate algebraic
method to prove or disprove simple
geometric theorems given a set of
coordinates.
-Use the slope to determine if lines
in a polygon are parallel.
-Use the Pythagorean Theorem to
determine if the point (a,b) lies on a
circle centered at the origin and
containing the point (x,y).
Note: Any italicized text denotes portions of a given standard that do not apply to identified standard content in this unit.
Resources/Exemplar Tasks:
( list possible task/activities students could engage in within this unit)
Standards for Mathematical Practice:
(highlight practice standards to be emphasized in the instructional unit)
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of instruction.
8. Look for and express regularity in repeated reasoning.
( BA: Broken Arrow rigor standard; PASS: Priority Academic Student Skills standard; BA/PASS: Combination standard )