Back to Prove triangles congruent — Problem 2 · 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.

$Triangle PQR mapped to triangle XYZ by a rigid motion, with corresponding sides PQ and XY marked.$

A rigid motion maps $\triangle PQR$ onto $\triangle XYZ$ with $P \mapsto X$ , $Q \mapsto Y$ , $R \mapsto Z$ . Which statement is justified by the forward direction of the biconditional?

$PQ = XY$ because the rigid motion maps $P$ to $X$ and $Q$ to $Y$ , and rigid motions preserve distances.

$PQ = XY$ because both segments are sides of triangles.

$\angle P = \angle X$ because they are the first-listed angles in their respective triangles.

$PR = XZ$ because both triangles have the same shape.