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All courses Geometry · G-CO.8 10 of 57
Explain ASA, SAS, and SSS triangle congruence criteria from rigid-motion congruence.

Classify triangle congruence evidence

Problem
What congruence criterion, if any, is shown by these diagram marks: \(\text{three}\) pairs of corresponding sides marked congruent?
Marked triangle diagram showing only the geometric facts supplied in the problem. Open full size
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Hint

Count how many side pairs are marked congruent.

Three matching side pairs correspond to the SSS criterion.

Solution walkthrough

01

Count the marked side pairs

\[AB~\text{corresponds}~\text{to}~DE;~BC~\text{corresponds}~\text{to}~EF;~AC~\text{corresponds}~\text{to}~DF\]

The inspected diagram uses matching colors to identify all three corresponding side pairs.

02

Translate the evidence into a pattern

\[\text{side}-\text{side}-\text{side}\]

There are three side facts and no angle fact is needed for the displayed criterion.

03

Name the criterion

\[SSS\]

Three congruent corresponding side pairs form the Side-Side-Side congruence criterion.

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Another way

  1. Read the three colored edges of the first triangle and match each to the same-colored edge of the second triangle.

!

Common mistake

Do not call the marks SAS merely because SAS is a familiar criterion; no angle is marked in this evidence set.

Annotated triangle proof diagram identifying the valid criterion, missing fact, invalid step, or CPCTC conclusion.
criterion: SSS

Solution walkthrough video