Math 2
Lesson 4-3: Triangle Congruency and Similarity Theorems
Name_____________________________
Date ___________________________
Learning goals:
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I can show and explain that when two angle measures are known (AA), the third angle measure is also known (Third
Angle Theorem).
I can conclude and explain that AA as well as SSS and SAS are sufficient conditions for two triangles to be similar.
I can demonstrate that in a pair of similar triangles, corresponding angles are congruent (angle measure is preserved)
and corresponding sides are proportional.
I can define similarity as a composition of rigid motions following by dilations in which angle measure is preserved and
side length is proportional.
In this lesson, you will be looking for short-cuts to show that two triangles
are similar and/or congruent.
Open up the following Nspire document: Lesson 4-3 Triangle Congruency and Similarity Theorems.
Beginning with page 1.1, you will see two triangles. The triangle on the left was created with the conditions
from #1 listed below. You will be manipulating the triangle on the right. Your task is to “grab” (ctrl-click)
the green vertex of the triangle and drag it so that its corresponding measurements match those that are
given for the triangle on the left. Once you have done so, de-select the green vertex by pressing the click
button. Now compare the two triangles and then check the appropriate box(es) below them.
Move on to the next page and repeat the process.
1. m ∠ A = 48o
AB = 8.7 cm
m ∠ B = 67 o
See if it is possible to make additional triangles with the same corresponding measures. Were you able to do so? _____
2. m ∠ A = 80 o
AB = 7.3 cm
See if it is possible to make additional triangles with the same corresponding measures. Were you able to do so? _____
3. m ∠ A = 15 o
AB = 8.1 cm
BC = 2.7 cm
See if it is possible to make additional triangles with the same corresponding measures. Were you able to do so? _____
4. AB = 6.9 cm
BC = 5.7 cm
CA = 7.5 cm
See if it is possible to make additional triangles with the same corresponding measures. Were you able to do so? _____
5. AB = 5.5 cm
m ∠ B = 131 o
BC = 7 cm
See if it is possible to make additional triangles with the same corresponding measures. Were you able to do so? _____
6. m ∠ A = 68 o
m ∠ B = 56 o
See if it is possible to make additional triangles with the same corresponding measures. Were you able to do so? _____
7. AB = 8.5 cm
BC = 7 cm
See if it is possible to make additional triangles with the same corresponding measures. Were you able to do so? _____
Summary of Findings:
Problem
Number
1
2
3
4
5
6
7
Given Conditions
' s similar  ~ 
(Yes or no)
' s congruent   
(Yes or no)
Theorem
OVER 
Triangle Similarity Theorems:
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Similarity Statement: ___________________________
If ALL of the sides of two triangles are in proportion, then the triangles are similar.
Similarity Statement: ___________________________
If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles
are in proportion, then the triangles are similar
Similarity Statement: __________________________