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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

Congruence Statements

When stating that two triangles are congruent, the corresponding parts must be written in the same order. For example, if we know that ABC and LMN are congruent then we know that:

Notice that the congruent sides also line up within the congruence statement.

AB¯¯¯¯¯¯¯¯LM¯¯¯¯¯¯¯¯¯, BC¯¯¯¯¯¯¯¯MN¯¯¯¯¯¯¯¯¯¯, AC¯¯¯¯¯¯¯¯LN¯¯¯¯¯¯¯¯

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

ACBLNMCBANMLBCAMNLCABNLMBACMLN

What if you were told that FGHXYZ? How could you determine which side in XYZ is congruent to GH¯¯¯¯¯¯¯¯ and which angle is congruent to F?

Examples

Example 1

If ABCDEF, what else do you know?

From this congruence statement, we know three pairs of angles and three pairs of sides are congruent. AD,BE,CF, AB¯¯¯¯¯¯¯¯DE¯¯¯¯¯¯¯¯, BC¯¯¯¯¯¯¯¯EF¯¯¯¯¯¯¯¯, AC¯¯¯¯¯¯¯¯DF¯¯¯¯¯¯¯¯.

Example 2

If KBPMRS, what else do you know?

From this congruence statement, we know three pairs of angles and three pairs of sides are congruent. KM,BR,PS, KB¯¯¯¯¯¯¯¯MR¯¯¯¯¯¯¯¯¯, BP¯¯¯¯¯¯¯¯RS¯¯¯¯¯¯¯, KP¯¯¯¯¯¯¯¯MS¯¯¯¯¯¯¯¯¯.

Example 3

Write a congruence statement for the two triangles below.

Line up the corresponding angles in the triangles:

RF, SE, and TD.

Therefore, one possible congruence statement is RSTFED

Example 4

If CATDOG, what else do you know?

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

Example 5

If BUGANT, what angle is congruent to N?

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

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 below are congruent. Write a congruence statement for these triangles.
  2. Explain how we know that if the two triangles are congruent, then BZ.
  3. If TBSFAM, what else do you know?
  4. If PAMSTE, what else do you know?
  5. If INTWEB, what else do you know?
  6. If ADGBCE, what angle is congruent to G?

Review (Answers)

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

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