Geometry Unit 3 Congruence and Triangles
Enduring understanding (Big Idea): Students will understand that a) you can determine if 2 figures are congruent by
comparing corresponding parts b) triangles can be proven congruent without having to compare all corresponding parts c) the
angles and sides of Isosceles and Equilateral triangles have special relationships.
Essential Questions:
1) How do you identify corresponding parts of congruent triangles? 2) How do you show that 2 triangles are congruent? 3)
How can you tell whether a triangle is isosceles or equilateral? 4) How do you solve problems that involve measurements of
triangles?
BY THE END OF THIS UNIT:
Students will know…
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
that two figures are congruent if a series of rigid motions
carries one onto the other.
that two triangles are congruent if all corresponding pairs
of sides are congruent and all corresponding pairs of
angles are congruent.
Vocabulary: base angles of isosceles triangles, base, legs, and vertex of
isos. triangle, congruent polygons, corollary, hypotenuse, legs of rt
triangle, centroid, circumcenter, concurrent, equidistant, incenter,
median, midsegment and altitude of a triangle, orthocenter, bisector
Unit Resources
Students will be able to…
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use the definition of congruence in terms of rigid motions to
show that two triangles are congruent if and only if
corresponding pairs of sides and corresponding pairs of angles
are congruent.
explain how the criteria for triangle congruence (ASA, SAS, and
SSS) follow from the definition of congruence in terms of rigid
motions.
Use properties of midsegments to solve problems
Use properties of perpendicular and angle bisectors to solve
problems
Use properties of medians and altitudes to solve problems
Mathematical Practices in Focus:
Learning Task: Intro to Triangle Congruence
Performance Task: From CMS Wikispaces
Project: fettuccine noodles construction project
Online interactive website: students can click and drag
To form congruent triangles
Unit Review Game: Jeopardy Style Game
 Make sense of problems and persevere in solving them
 Construct viable arguments and critique the reasoning
of others
 Look for and express regularity in repeated reasoning
Standards on successive pages were unpacked by Utah State Office of Education, CMS-district specific modifications and resources for this unit were created by CMS teacher leaders. Standards are
listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes.
Geometry Unit 3 Congruence and Triangles
CORE CONTENT:
Cluster Title: Congruence-Prove Theorems about Triangles
Standard G-CO.10 Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the
segment joining midpoints of 2 sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Concepts and Skills to Master
 Use parallel lines to prove a theorem about triangles
 Find measures of angles in triangles
 Prove right triangles congruent using the Hypotenuse-Leg Theorem
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 The sum of the angle measures of triangles is always the same i.e. 180 degrees
 Understanding the parts of a right triangle
Academic Vocabulary
Exterior angle, remote interior angle, auxiliary line, hypotenuse, legs
Suggested Instructional Strategies

Use a number of examples with exterior angles and show how the 2
remote angles add up to the exterior angle. Draw the correlation
between triangle interior angles totaling 180° and an exterior angle
and its linear pair inside the triangle totaling 180°
Sample Formative Assessment Tasks
Skill-based task
Pearson website Lesson 3.5 Enrichment
Resources
 Textbook Correlation: Pearson 3.5, 4.1, 4.2, 4.3, 4.5, 4.6,
5.1, 5.4
 Video resource: Introduction Congruent Triangles
Problem Task
Pearson website Activities, Games and Puzzles 3.5
Standards on successive pages were unpacked by Utah State Office of Education, CMS-district specific modifications and resources for this unit were created by CMS teacher leaders. Standards are
listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes.
Geometry Unit 3 Congruence and Triangles
Pearson Solve it! 3.5
Pearson website Lesson 4.5 Enrichment (Swan Puzzle)
CORE CONTENT:
Cluster Title: Congruence
Standard G-CO.7 -Use the definition of congruence in terms of rigid motion to show that 2 triangles are congruent if and only
if corresponding pairs of sides and corresponding pairs of angles are congruent.
Concepts and Skills to Master
 Recognize congruent figures and their corresponding parts
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Proving angles congruent
Academic Vocabulary
Congruent polygons
Suggested Instructional Strategies
Resources
 Have students draw the given figures so that each is
 Textbook Correlation: Pearson Chapter 4.1
oriented the same way
 Have students “work backwards” in the proof, i.e.
start with the desired conclusion work backwards to
identify information given and needed
Sample Formative Assessment Tasks
Skill-based task
Complete the following statements:
Given: ΔQXR ΔNYC
a) line segment QX
Problem Task
If each angle in one triangle is congruent to its corresponding angle
in another triangle, are the two triangles congruent? Explain.
line segment _?_
Standards on successive pages were unpacked by Utah State Office of Education, CMS-district specific modifications and resources for this unit were created by CMS teacher leaders. Standards are
listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes.
Geometry Unit 3 Congruence and Triangles
b)
Y
_?_
CORE CONTENT:
Cluster Title: CongruenceStandard G-CO.8- Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
Concepts and Skills to Master
 Prove 2 triangles congruent using ASA, SAS, AAS, SSS, and HL Theorem
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Parts of a right triangle and congruent corresponding parts
Academic Vocabulary
congruent triangles, hypotenuse, legs of a right triangle
Suggested Instructional Strategies
 Point out that for SAS the included angle MUST be
between the 2 sides used in the proof
 Likewise, for ASA the included side MUST be between
the 2 angles used in the proof
 Point out that ASS is NOT method of proving triangles
congruent nor is AAA. However, in a right triangle,
what students see as ASS can often be HL.
Resources
 Textbook Correlation: Pearson Chapter 4.2, 4.3, 4.6
Sample Formative Assessment Tasks
Standards on successive pages were unpacked by Utah State Office of Education, CMS-district specific modifications and resources for this unit were created by CMS teacher leaders. Standards are
listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes.
Geometry Unit 3 Congruence and Triangles
Skill-based task
Problem Task
Pearson Additional Problems
Draw and label three pairs of triangles to illustrate the SideSide-Side, Angle-Side-Angle, and Side-Angle-Side
Postulates. One pair of triangles should share a common
side. The figures should provide enough information to prove
that they are congruent. Write the congruence statements for
each pair.
Teacher Created Argumentation Tasks (W1-MP3&6)
What types of conditions help you to decide which method of triangle congruency to use when writing a proof? After reading the Prentice Hall text
sections on writing proofs for proving triangles congruent, listening in class to class instructions and demonstrations, and using the Prentice Hall CD
Rom resources to read and listen along to information regarding writing proofs to prove triangle congruency, write a letter to a friend that was absent
multiple days in class that compares using ASA, AAS, SSS, SAS, and HL Theorem and argue what method is best to use. Include what types of
conditions help you decide which method to use. Be sure to support your position with evidence from any of the texts.
Standards on successive pages were unpacked by Utah State Office of Education, CMS-district specific modifications and resources for this unit were created by CMS teacher leaders. Standards are
listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes.