Back to Use rigid motions for congruence — Problem 4 · Task Set 6

Exercises: Use Rigid Motions to Define and Determine Congruence

Work through each section in order. For problems that ask you to find a rigid motion, verify your answer by checking every vertex.

Grade 9·20 problems·~30 min·Common Core Math - HS Geometry·standard·hsg-co-b-6

Work through problems with immediate feedback

Fluency Practice

Apply rigid motions and the definition of congruence to answer each problem.

Triangle $ABC$ has vertices $A(0, 0)$ , $B(3, 0)$ , $C(0, 4)$ .
A student claims that to verify a rigid motion maps $ABC$ to a target triangle,
it is sufficient to check that the three vertex images match the three target vertices.
Is this claim correct?

No — every point on every side must be checked individually

No — only the midpoints of each side need to be checked in addition
to the vertices

Yes — rigid motions map line segments to line segments, so if all vertices
match, all points on the sides automatically match

Yes — but only for triangles; for quadrilaterals, you must check diagonals
as well