SAS® Curriculum Pathways®
Mathematics 1450
Triangles: Proving Congruency: In-class Worksheet (High School)
NAME(S):
CLASS:
DATE:
Review
► Suppose
DOG 
CAT . Complete the following congruent parts:
1) D 
2) O 
3) G 
4) DO 
5) OG 
6) DG 
Demo: Understanding the Postulates and Theorem .............................................................
Use the Geometry Tool on the computer to watch the demo. Then use what you learn to write a brief response for
Problems 7 – 10.
7) Write the abbreviated names of the postulates and theorem from the six cases listed in the demo that can be
used to prove two triangles are congruent.
8) Explain what is meant by the included angle in the SAS postulate and the included side in the ASA postulate.
9) Is it correct to state that if two sides and an angle of one triangle are congruent to two sides and an angle of
another triangle, then the triangles are congruent? Why or why not?
10) Knowing that the three angles of one triangle are congruent to the three angles of another triangle does not
provide enough information to show the triangles are congruent. Explain why.
Practice: Applying the Concepts ................................................................................................
For Problems 11 – 16, use the Practice section of the Geometry Tool ON THE COMPUTER to follow these steps:
a) Be sure SYMBOLIC mode is selected.
E
b) Name the first triangle DEF.
c) Create a triangle shaped like this one:
d) Click
D
F
to show a second triangle for comparison.
e) Answer the question on the computer, “Can the triangles be proven congruent?” by selecting “yes” or “no.”
If you select “yes”, complete the Congruence Statement.
f)
Use
to check your answers. Correct any mistakes and check your answers again.
g) If the triangles ARE congruent, complete sketches for both triangles below. Include their symbolic markings.
Then write the Congruence Statement, including the postulate or theorem.
h) If the triangles are NOT congruent, click
First Triangle
Second Triangle
E
F
D
Congruence Statement:
until you get two congruent triangles.
DEF 
by postulate or theorem
Copyright © 2011, SAS Institute Inc., Cary, NC, USA, All Rights Reserved
3/1/2011
Page 1 of 2
SAS® Curriculum Pathways®
Mathematics 1450
Triangles: Proving Congruency: In-class Worksheet (High School)
► Using the directions from the previous page, complete Problems 11 – 14 below. When you create the first
triangle in each problem, give it a different name and draw triangles of differing shapes, including scalene,
isosceles, right, obtuse, etc.
First Triangle
Second Triangle
11)
First Triangle
Second Triangle
12)
Congruence Statement:
First Triangle
Congruence Statement:
Second Triangle
13)
First Triangle
Second Triangle
14)
Congruence Statement:
Congruence Statement:
► For Problems 15 – 16, select NUMERIC mode. Continue to create triangles with different names and shapes.
First Triangle
Second Triangle
15)
First Triangle
Second Triangle
16)
Congruence Statement:
Congruence Statement:
Proof: Extending the Reasoning .................................................................................................
Use the Proof section of the Geometry Tool on the computer to complete the online proof. Check your answers.
Then answer the following question.
17) Which one of the congruence postulates is being used to prove this theorem?
Copyright © 2011, SAS Institute Inc., Cary, NC, USA, All Rights Reserved
3/1/2011
Page 2 of 2