Back to Explain triangle congruence criteria — Problem 3 · Task Set 8

Exercises: Triangle Congruence Criteria from Rigid Motions

Work through each section in order. For explanation problems, use complete sentences and reference rigid motions where relevant.

Grade 9·21 problems·~30 min·Common Core Math - HS Geometry·standard·hsg-co-b-8

Work through problems with immediate feedback

Fluency Practice

In the ASA proof, after aligning side $\overline{AB}$ onto $\overline{DE}$ (so $A'' = D$ and $B'' = E$ ), why is vertex $C''$ uniquely determined as $F$ ?

The side $AC = DF$ places $C''$ at the correct distance from $D$ .

The angle at $A$ forces ray $DC''$ onto ray $DF$ , and the angle at $B$ forces ray $EC''$ onto ray $EF$ ; their intersection is uniquely $F$ .

Two circles centered at $D$ and $E$ with radii $DF$ and $EF$ intersect at $F$ .

The third angle $\angle C = \angle F$ is automatically equal, forcing the vertex to coincide.