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Congruence Statements

Learn how to write congruence statements and use congruence statements to determine the corresponding parts of triangles.

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Congruence Statements

What if you were told that ? How could you determine which side in is congruent to and which angle is congruent to

Congruence Statements 

When stating that two triangles are congruent, use a congruence statement. The order of the letters is very important, as corresponding parts must be written in the same order. Notice that the congruent sides also line up within the congruence statement.

We can also write this congruence statement several other ways, as long as the congruent angles match up. For example, we can also write as:

One congruence statement can always be written six ways. Any of the six ways above would be correct.

Watch the first part of this video.

Writing a Congruence Statement 

Write a congruence statement for the two triangles below.

To write the congruence statement, you need to line up the corresponding parts in the triangles: and . Therefore, the triangles are .

Making Conclusions from Congruence Statements 

If , what else do you know?

From this congruence statement, we can conclude three pairs of angles and three pairs of sides are congruent.

Finding Congruent Angles 

If , what angle is congruent to ?

Since the order of the letters in the congruence statement tells us which angles are congruent, because they are each the second of the three letters.

Earlier Problem Revisited

If , then and .

Examples

Example 1

If , what else do you know?

From this congruence statement, we know three pairs of angles and three pairs of sides are congruent. ,

Example 2

If , what else do you know?

From this congruence statement, we know three pairs of angles and three pairs of sides are congruent. 

Example 3

If , what else do you know?

From this congruence statement, we know three pairs of angles and three pairs of sides are congruent. , .

Review 

For questions 1-4, determine if the triangles are congruent using the definition of congruent triangles. If they are, write the congruence statement.

  1. Suppose the two triangles to the right are congruent. Write a congruence statement for these triangles.
  2. Explain how we know that if the two triangles are congruent, then .

Suppose .

  1. What angle is congruent to ?
  2. What side is congruent to ?
  3. What side is congruent to ?

Suppose .

  1. What side is congruent to ?
  2. What angle is congruent to ?
  3. What angle is congruent to ?

Suppose .

  1. What side is congruent to ?
  2. What side is congruent to ?
  3. What angle is congruent to ?

Review (Answers)

To view the Review answers, open this PDF file and look for section 4.4. 

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