Understanding By Design Unit Template
Title of Unit
Curriculum Area
Developed By
Congruent Figures
Mathematics - Geometry
Molly Steffee
Grade Level
Time Frame
9th/10th/11th
12 days
Identify Desired Results (Stage 1)
Content Standards
CCSS.Math.Content.HSG.CO.B.7
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
CCSS.Math.Content.HSG.SRT.B.4
Prove theorems about triangles
Understandings
Essential Questions
Overarching Understanding
Overarching
Students will understand that they can use previous knowledge of angles and lines
and problem solving skills to make conclusions about triangles and to determine if two
triangles are congruent.
Students will understand the importance of gathering all known information before
starting to prove something is true.
Students will understand how a proof is broken down into parts: the given, the body
of the proof, and the end/what they are proving.
Students will understand how to justify their conclusions via definitions and theorems.
 How do proofs connect to
what we have learned so far?
 In what real world situation
is this mathematics useful?
 What strategies can I use
when solving a proof?
Related Misconceptions
Not understanding what conclusions they can make given certain information, or from
conclusions they have already made, or from a given figure.
Not understanding the differences between triangle congruence theorems (such as
the difference between AAS and ASA)
Not understanding how to justify the conclusions they make in the body of a proof.
Not understanding how to correctly sequence their conclusions in their proof.
Objectives
Knowledge
Skills
Students will know…
Students will be able to…
Topical
 What is the difference
between justifying your answer
and proving something is true?
 When are proofs used?
 How can I use proofs to
make conclusions from given
information?
-Students will know the different parts of a proof.
-Students will know the Triangle Congruence Theorems and Postulates.
-Students will know the different parts of a right triangle (hypotenuse, legs, one 90
degree angle)
-Students will know the different parts of an isosceles triangle (legs, base, vertex
angle and base angles).
-Students will know which corresponding parts of congruent triangles are congruent.
-Students will know how to make conclusions based upon given information.
-Students will be able to prove two triangles are congruent based
upon given information and Triangle Congruence
Theorems/Postulates
-Students will be able to conclude what parts are congruent on
two congruent polygons
-Students will be able to use what they have learned about
triangles (specifically isosceles and right triangles) to solve for an
angle or side.
- Students will be able to explain the difference between the
Triangle Congruence Theorems,
-Students will be able to draw conclusions from two congruent
triangles
Assessment Evidence (Stage 2)
Performance Task Description: Unit Test
Goal
Role
Audience
Situation
Product/Performance
Standards
Students will demonstrate their understanding of Triangle Congruence Theorems and Postulates, and they will
be able to use them to prove two triangles are congruent. Students will be able to draw conclusions from
congruent triangles. Students will be able to use information about isosceles and right triangles to solve for a
specific angle in the triangle. Students will be able to conclude what parts of congruent polygons are
congruent.
Unit Test
Myself, Mentor Teacher (Tina Ely)
Classroom Test; Regular Class Period
Completed Test
CCSS.Math.Content.HSG.CO.B.7
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
CCSS.Math.Content.HSG.SRT.B.4
Prove theorems about triangles
Other Evidence
Quizzes (2) – One quiz will be during the first week of the unit, and it will contain questions that will ask for student understanding of the Triangle
Congruence Theorems. The other quiz will contain questions that ask students either to prove two triangles are congruent, or to prove two corresponding
parts on a triangle are congruent.
Exit Passes – See assessment activities for questions
Learning Plan (Stage 3)
Day in Unit
Lesson Topic
Lesson Learning
Description of how lesson
Assessment activities
Objective
1
Congruent Figures
– Naming
congruent parts of
a polygon
SWBAT recognize congruent
figures and their corresponding
parts
contributes to unit-level
objectives
This lesson ensures that students
understand that congruent
polygons have congruent
corresponding parts (their
matching sides and angles)
This lesson will help them later in
the unit, when they are asked to
prove two triangles are congruent.
Exit Slip: Given two polygons,
students will be asked to find 3
pairs of congruent sides and 3 pairs
of congruent angles.
Exit Pass: Students will be given
pairs of triangles, and will be asked
if they can conclude that they are
congruent. If they can conclude
they are congruent, they have to
justify their answer using SSS or
SAS.
Exit Pass: Students will be given
pairs of triangles, and they will be
asked to determine if two triangles
are congruent (by using the two
new Triangle Congruence
Theorems they learned today). If
the two triangles are congruent,
they will have to justify their
answer with a Triangle Congruence
Postulate/Theorem.
Meets the following unit objective:
Students will be able to determine
which corresponding parts of a
congruent polygon are congruent.
2
Understanding the
Triangle
Congruence
Postulates – SSS &
SAS
SWBAT determine if two triangles
are congruent by using the SSS
and SAS postulates.
Partially meets the following unit
objective: Students will be able to
explain Triangle Congruence
Postulates/Theorems, and will be
able to use them to determine if
two triangles are congruent.
3
Understanding the
Triangle
Congruence
Postulate/Theorem
– ASA and AAS
SWBAT determine if two triangles
are congruent by using the ASA
Postulate and the AAS Theorem.
Partially meets the following unit
objective: Students will be able to
explain Triangle Congruence
Postulates/Theorems, and will be
able to use them to determine if
two triangles are congruent.
Teaching Experiment: (Let the
Chalk do the Talk) – I will give
pairs of students one problem. The
problem will contain 10 triangles,
and they have to find pairs of
congruent triangles, and explain
why they are congruent by using
Triangle Congruence
Theorems/Postulates.
4
Using Congruent
Triangles to make
conclusions about
their other parts
(CPCTC)
SWBAT determine which
corresponding parts of congruent
triangles are congruent.
Meets the following unit objective:
Students will be able to determine
which parts of a congruent
polygon are congruent.
5
Proof Introduction
Day
SWBAT explain the difference
between the different parts of a
proof.
Students will also be able to make
conclusions based upon given
information and what they have
learned so far in Geometry.
This lesson ensures that students
understand how to set up a proof.
This will be helpful for the next
two lessons in the unit, where
students will be asked to prove
triangles are congruent.
Meets the following unit objective:
Students will be able to make
conclusions based on given
information about a polygon, and
they will be able to justify their
conclusions using
Theorems/Postulates we have
learned thus far in Geometry.
6
Proving two
triangles are
congruent using
SSS, SAS, AAS and
ASA
SWBAT prove two triangles are
congruent (through flow proofs,
paragraph proofs, or two-column
proofs) by using TriangleCongruence Theorems.
7
Using CPCTC to
prove that two
parts of a triangle
are congruent
SWBAT prove two corresponding
parts of a triangle are congruent,
by first proving two triangles are
congruent.
Meets the following unit objective:
Students will be able to prove two
triangles are congruent (through
flow proofs, paragraph proofs or
two-column proofs) by using
Triangle-Congruence Theorems.
Meets the following unit objective:
students will be able to determine
which corresponding parts of a
congruent polygon are congruent.
8
Right/Isosceles
Triangles
SWBAT determine the different
parts of right and isosceles
triangles. Students will also be
able to explain and use the
Meets the following unit objective:
Students will be able to explain
Triangle Congruence
Postulates/Theorems, and will be
Quiz: Students will be given pairs
of triangles, and they will be asked
if they can conclude the triangles
are congruent. If they can conclude
they are congruent, they will be
asked to justify their answer by
using one of the Triangle
Congruence Postulates/Theorems.
Exit Pass: Students will be given
information about a figure, and
they will have to make conclusions
based upon the information they
are given.
Exit Pass Sample Question:
Name three conclusions you make
about the following figure:
-A regular pentagon
(It has equal angles, equal sides, 5
sides total, it’s a polygon)
Exit Pass: Students will be given
two triangles with given
information about the triangles,
and they will have to prove via a
proof that the two triangles are
congruent.
Quiz: Students will be given 3-4
triangles with some parts known to
be congruent, and they will be
asked to prove the two triangles
are congruent, or to prove
corresponding parts on a triangle
are congruent.
Exit Pass: Question 1) Students will
be given two right triangles, with
the corresponding legs labeled as
congruent, and they will be asked
Hypotenuse-Leg theorem to
prove that two right triangles are
congruent.
able to use them to determine if
two triangles are congruent.
to prove that the two right triangles
are congruent.
Students will be able to
determine angle measures of
isosceles and right triangles
by using properties of
isosceles and right triangles.
9
Review
Review
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10
Review
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Review
11
Test
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Test