Use Definition of Congruence to Show that two Triangles are Congruent
P202
Standard
SM1 Section 9-1
Date:_____________
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.
Objectives
Identify corresponding parts of two triangles
Show that two triangles are congruent if and only if corresponding angles are congruent and corresponding sides are congruent.
Vocabulary
Congruence
Corresponding sides
Corresponding angles
Definitions
Congruent polygons have exactly the same size and shape.
When two figures are congruent, there is a correspondence between their angles and sides, such that corresponding angles are congruent and corresponding sides are congruent.
For the triangles below, you can write
, which is read “triangle ABC is congruent to triangle FED”. The notation shows the congruence and the correspondence.
There is more than one way to write a congruent statement, but it is important to list the corresponding angles in the same order. For example, you can also write.

EXAMPLE 1. Naming congruent parts.
The congruent triangles represent the triangles in the picture below. Write a congruence statement. Identify all pairs of congruent corresponding parts.
Writing a Congruence Statement means to write the corresponding angles in the same order.
EXAMPLE 2: From the picture in example 1, write the three possible congruent statements.
Solution: We know that, congruence statements: therefore, we can write the following
Notice that all the corresponding angles are in the same order.
Practice 1. The congruent triangles represent the triangles in the picture below.
Write a congruence statement and
Identify all pairs of congruent corresponding parts. (Angles and Sides)
Congruence Statement:
Angles Sides

EXAMPLE 2. Using properties of congruent figures.
In the diagram,
Find the missing angle measures or side length using the diagram above.
Solution:
Writing an equivalent congruence statement:
Solution:
To write a new congruence statement you put the corresponding angles in the same order as the first triangle in your statement:
Looking at the congruence statement above we can see that Y and N, X and
M, and Z and L are all corresponding (in the same position). So we can say:

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Practice 2:
Solve for x: