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Geometry
Lesson Activities
Sides and Angles of Congruent Triangles
The Lesson Activities will help you meet these educational goals:
 Content Knowledge—You will 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.
 Mathematical Practices—You will use appropriate tools strategically.
 Inquiry—You will perform an investigation in which you will communicate your
results in graphs and draw conclusions.
 21st Century Skills—You will carry out technology-assisted modeling.
Directions
Please save this document before you begin working on the assignment. Type your
answers directly in the document.
_________________________________________________________________________
Teacher-Graded Activities
Write a response for each of the following activities. Check the Evaluation section at the end
of this document to make sure you have met the expected criteria for the assignment. When
you have finished, submit your work to your teacher.
1. Congruent Triangles
In this activity, you will use the GeoGebra geometry tool to explore the relationships
among the sides and angles of congruent triangles. If you need help, follow these
instructions for using GeoGebra.
a. Transform  ABC in these ways:
 Translate  ABC by moving it 5 units to the right and 2 units up.
 Draw the line y = -x, and reflect  ABC across the line.
 Rotate  ABC counterclockwise about the origin by 270°.
When you’re through, capture the figure containing the preimage and the three images
and paste it in the space provided.
Type your response here:
b. Measure the angles of  ABC and its three images, and record the measurements in
the table. Round each answer to the nearest degree.
Type your response here:
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 ABC
 ABC
Measure  A'B'C'
 A'B'C'
 ACB
 A'C'B'
 CAB
 C'A'B'
Measure  A'1B'1C'1 Measure  A'2B'2C'2 Measure
 A'1B'1C'1
 A'2B'2C'2
 A'1C'1B'1
 A'2C'2B'2
 C'1A'1B'1
 C'2A'2B'2
c. Measure the lengths of the sides of  ABC and its three images, and record the
measurements in the table.
Type your response here:
 ABC
Measure  A'B'C'
Measure  A'1B'1C'1 Measure  A'2B'2C'2 Measure
AB
A'B'
A'1B'1
A'2B'2
BC
B'C'
B'1C'1
B'2C'2
AC
A'C'
A'1C'1
A'2C'2
d. How do the measures of the sides and angles of  ABC compare with the
corresponding measurements in the three images?
Type your response here:
e. Translations, rotations, and reflections are rigid transformations. What can you
conclude about the measures of sides and angles on any triangle after undergoing a
series of rigid transformations? Explain.
Type your response here:
f. By definition, two shapes are congruent if you can map one onto the other using rigid
transformations (a sequence of one or more rotations, translations, and reflections).
Since any sequence of rigid transformations performed on a triangle results in a
congruent triangle, what does that imply about the corresponding side lengths and
angle measures for two congruent triangles?
Type your response here:
g. If two triangles have three corresponding angles and three corresponding sides that
are equal in measure, are the two triangles necessarily congruent? Why?
Type your response here:
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Evaluation
Your teacher will use this rubric to evaluate the completeness of your work as well as the
clarity of thinking you exhibit.
Total Points: 100
Task 1: Congruent Triangles
Task points: 100
a. Transform  ABC.
30
b. Measure the angles of  ABC and its images.
10
c. Measure the sides of  ABC and its images.
10
d. Draw conclusions about the sides and angles of  ABC.
15
e. Extend concepts from  ABC to all triangles.
10
10
f.
Define triangle congruency in terms of sides and angles.
15
g. Develop a converse statement for triangle congruency.
3