Back to Prove triangles congruent — Problem 4 · Task Set 7

Exercises: Prove Triangles Congruent Using Rigid Motions

Work through each section in order. Show your reasoning where indicated.

Grade 9·20 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-co-b-7

Work through problems with immediate feedback

Fluency Practice

Apply the biconditional and CPCTC directly.

Two triangles have the following measurements. Triangle $ABC$ : $AB = 5$ , $BC = 7$ , $AC = 6$ , $\angle A = 82^\circ$ , $\angle B = 55^\circ$ , $\angle C = 43^\circ$ . Triangle $DEF$ : $DE = 5$ , $EF = 7$ , $DF = 6$ , $\angle D = 82^\circ$ , $\angle E = 55^\circ$ , $\angle F = 43^\circ$ . What does the biconditional guarantee?

The triangles might be congruent, but we need more information.

$\triangle ABC \cong \triangle DEF$ because all six corresponding parts are equal.

The triangles are similar but not necessarily congruent.

We can only conclude congruence after finding an explicit rigid motion.