North East School Division
Unpacking Outcomes
Unpacking the Outcome
Demonstrate understanding (properties of angles and triangles) by including:
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deriving proofs based on theorems and postulates about congruent triangles
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solving problems.
Outcome (circle the verb and underline the qualifiers)
FM 20.4 Demonstrate understanding of properties of angles and triangles including:
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deriving proofs based on theorems and postulates about congruent triangles
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solving problems.
KNOW
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Vocab – parallel lines
Transversals
Theorem
Postulate
Congruent
parallel, perpendicular, transversal, angle,
line, bisect, corresponding, vertically
opposite, alternate interior, alternate
exterior, same side exterior and interior,
complimentary, supplementary, Mira,
protractor, compass, straightedge, square,
acute, right, straight, obtuse, reflex,
orientation of angles, axial symmetry,
planes
Angles in a Triangle
Names of Different Polygons
UNDERSTAND
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relationships between
angles formed when a
transversal intersects
parallel lines
different polygons
That shapes may be
classified in multiple
categories; for example,
a rectangle is also a
parallelogram.
That corresponding
angles are equal,
alternate interior angles
are equal, and alternate
exterior angles are
equal.
How to determine
angles in a diagram
BE ABLE TO DO
a. Identify and describe situations relevant to
self, family, or community that involve
parallel lines cut by transversals.
b. Develop, generalize, explain, apply, and prove
relationships between pairs of angles formed
by transversals and parallel lines, with and
without the use of technology.
c. Prove and apply the relationship relating the
sum of the angles in a triangle.
d. Generalize, using inductive reasoning, a rule
for the relationship between the sum of the
interior angles and the number of sides (n) in
a polygon, with or without technology.
e. Apply knowledge of angles formed by parallel
lines and transversals to identify and correct
Drawing angles
Replicating  angles
Constructing  angles
Bisecting  angles
Relating  angles to lines (parallel,
perpendicular, transversal)
Identify and sort quadrilaterals and triangles
according to their properties.
Determine if polygons are similar, and explain the
reasoning.
Demonstrate congruence in a regular polygon by
measuring.
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based upon knowing
only measure of an
angle.
That two lines are not
parallel if corresponding
angles are not equal.
That the supporting
statements in a proof
are as important as the
statement itself.
errors in a given proof.
f. Explore and verify whether or not the angles
formed by non-parallel lines and transversals
create the same angle relationships as those
created by parallel lines and transversals.
g. Solve situational problems that involve:
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angles, parallel lines, and transversals
angles, non-parallel lines, and transversals
angles in triangles
angles in polygons.
h. Develop, generalize, explain, and apply
strategies for constructing parallel lines.
ESSENTIAL QUESTIONS
• What are Parallel Lines?
 How do angles within a shape affect each other?
 What pieces of information are important when solving problems involving angles? What tools are necessary?
 Why is measuring angles important?
 How can special angles be used in problem solving?
 How are lines and angles inter-related?
 How does recognizing patterns between lines and angles make measuring and identifying angle sizes easier?
 Why are the terms parallel and perpendicular so important?
 What is the relationship between the orientation of angles and how we measure or replicate them?
 What strategies can I use to solve problems involving angles?
 Why are patterns important?
 What is the language of angles?
 How can you use angles to determine if lines are parallel?
 How does drawing a diagram help you complete a proof?