Back to Explain triangle congruence criteria — Problem 4 · 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

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Fluency Practice

In $\triangle ABC$ and $\triangle DEF$ , you know $\angle A \cong \angle D$ , $\angle C \cong \angle F$ , and $\overline{BC} \cong \overline{EF}$ . This is AAS (two angles and a non-included side). Which statement correctly explains why these triangles must be congruent?

AAS is a separate valid criterion, proved independently of ASA.

AAS does not guarantee congruence because the side is not included between the two angles.

Since $\angle A + \angle C + \angle B = 180^\circ$ and $\angle D + \angle F + \angle E = 180^\circ$ , we get $\angle B \cong \angle E$ ; now $\angle B \cong \angle E$ , $\overline{BC} \cong \overline{EF}$ , and $\angle C \cong \angle F$ is ASA applied to side $\overline{BC}$ .

AAS fails like SSA because neither has the side between the two known angles.