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All courses Math I · G-CO.7 42 of 59
Use rigid motions to show triangle congruence through corresponding sides and angles.

Identify corresponding sides and angles from congruence notation

Problem
In the congruence statement triangle ABC congruent to triangle DEF, identify the corresponding sides and angles.
Triangle or coordinate diagram presenting only the geometric data supplied in the prompt. Open full size
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Hint

Read the congruence statement in order so the first letters match, the second letters match, and the third letters match.

In a congruence statement, corresponding vertices are listed in matching positions.

Solution walkthrough

01

Read corresponding vertices

\[A~\text{corresponds}~\text{to}~D;~B~\text{corresponds}~\text{to}~E;~C~\text{corresponds}~\text{to}~F\]

The inspected congruence diagram places A, B, C in the same relative positions as D, E, F.

02

Form the angle pairs

\[A=D;~B=E;~C=F\]

Corresponding vertices determine the corresponding angles.

03

Form the side pairs

\[AB=DE;~BC=EF;~AC=DF\]

A side corresponds to the side joining the partners of its two endpoints.

04

Report every correspondence

\[\text{angles}:~A=D,~B=E,~C=F;~\text{sides}:~AB=DE,~BC=EF,~AC=DF\]

The answer lists all three corresponding angles and all three corresponding sides in the requested categories.

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Another way

  1. Write A B C above D E F, then build each angle and side pair column by column.

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Common mistake

Do not pair sides by how they look alone. Map both endpoints first; for example, B-C becomes E-F.

Annotated triangle diagram showing correspondence, congruence evidence, invariant, and conclusion.
corresponding angles: angle A=angle D, angle B=angle E, angle C=angle F; corresponding sides: AB=DE, BC=EF, AC=DF