Back to Explain triangle congruence criteria — Problem 2 · 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 SAS rigid-motion proof, after translating vertex $A$ to vertex $D$ and rotating so that $B$ maps to $E$ , what forces vertex $C''$ to land exactly on vertex $F$ ?

The included angle $\angle A \cong \angle D$ forces ray $DC''$ to point in the same direction as ray $DF$ , and the side length $AC = DF$ places $C''$ at the correct distance.

The triangle angle sum forces $\angle C'' = \angle F$ , which places $C''$ on $F$ .

Two circles centered at $D$ and $E$ intersect at $F$ , determining $C''$ .

A reflection over line $DE$ maps $C''$ to $F$ .