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CONGRUENT TRIANGLES
Look closely at the pairs of congruent triangles below. Determine which congruence test each pair satisfies. 
Then, label each pair and explain your answer in the space provided.
Write your 
explanation here.
Write your 
explanation here.
Write your 
explanation here.
Write your 
explanation here.
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[Congruence 
Test]
[Congruence 
Test]
[Congruence 
Test]
[Congruence 
Test]
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Page 2


CONGRUENT TRIANGLES
Look closely at the pairs of congruent triangles below. Determine which congruence test each pair satisfies. 
Then, label each pair and explain your answer in the space provided.
Write your 
explanation here.
Write your 
explanation here.
Write your 
explanation here.
Write your 
explanation here.
S
U
M
N
Q
P
R
O
T
K
L
J
[Congruence 
Test]
[Congruence 
Test]
[Congruence 
Test]
[Congruence 
Test]
A
B
C G
H
I
D E
F
Y X
Z
The pair of triangles
satisfies the RHS (Right
Angle-Hypotenuse-Side)
test because they are
right triangles with an
equal hypotenuse and 
a corresponding side.
CONGRUENT TRIANGLES
Look closely at the pairs of congruent triangles below. Determine which congruence test each pair satisfies. 
Then, label each pair and explain your answer in the space provided.
The pair of triangles
satisfy the SAS 
(Side-Angle-Side) test
because two pairs of
sides and their included
angles are equal.
The pair of triangles
satisfies the AAS 
(Angle-Angle-Side) 
test because two pairs
of angles and their
included sides are
equal.
The pair of triangles
satisfy the SSS 
(Side-Side-Side) test
because all of their
sides are equal.
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F
Y X
Z
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A N S W E R
K E Y
S S S A A S
S A S R H S
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FAQs on Visual Worksheet: Congruent Triangles - Mathematics Olympiad for Class 9

1. What are congruent triangles?
Ans.Congruent triangles are triangles that are identical in shape and size. This means that all corresponding sides and angles of the triangles are equal. If two triangles are congruent, one can be placed over the other, and they will match perfectly.
2. How can we determine if two triangles are congruent?
Ans.There are several methods to determine if two triangles are congruent, including the Side-Side-Side (SSS) criterion, where all three sides of one triangle are equal to the three sides of another triangle; the Side-Angle-Side (SAS) criterion, where two sides and the included angle of one triangle are equal to the corresponding parts of another triangle; and the Angle-Side-Angle (ASA) criterion, where two angles and the included side are equal.
3. What is the importance of congruent triangles in geometry?
Ans.Congruent triangles are important in geometry because they are used to prove various geometric properties and theorems. For example, they are essential in establishing the congruence of shapes and are used in real-world applications such as construction, design, and various fields of engineering.
4. Can congruent triangles have different orientations?
Ans.Yes, congruent triangles can have different orientations. They may be rotated, reflected, or translated in space, but as long as their corresponding sides and angles remain equal, the triangles are still considered congruent.
5. What are some real-life examples of congruent triangles?
Ans.Real-life examples of congruent triangles can be found in construction, where triangular supports or trusses are used. Additionally, in art and design, congruent triangles can be observed in patterns and structures, such as roofs or bridges, where uniformity is crucial for stability and aesthetics.
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