GOZUNTA
Try it now
All courses Math I · G-CO.8 43 of 59
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: three pairs of corresponding sides marked congruent?
Marked triangle diagram showing only the geometric facts supplied in the problem. Open full size
Your answer
Show answer choicesAnswer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Turn a few problems into a learning session.

Choose a course and objective, collect included problems into a session, and work through them in order.

Create a free account
With paid access

Take the session to paper.

Export learning sessions as spacious printable PDFs when pencil-and-paper practice works better.

Compare plans

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.

+

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