Question

what transformations always produce congruent figures? explain. What transformations only sometimes produce congruent figures? explain. Write an algebraic rule for a translation that moves a triangle 4 units to the right and 8 units up. What are the only times that a dilation will produce a congruent figure? explain.

Answer 1

The transformations that always produce congruent figures are TRANSLATIONS, REFLECTIONS, and ROTATIONS. These transformations are isometric, thus, the figures produced are always congruent to the original figures.

The transformation that sometimes produce congruent figures is dilation. It can be enlargement or contraction. 

rule: (x,y) → (x+4,y+8)