What can you say about two triangles that have three pairs of congruent sides?
They are congruent. See solution.
Practice makes perfect
From the diagram, we see that the triangles have three pairs of congruent sides. Therefore, we can claim that they are congruent by the Side-Side-Side Congruence Theorem. To prove this, we will use rigid motions to map one triangle onto the other.
Mapping one onto the other
Note that ∠D and ∠H are both between the same two pairs of corresponding sides. This means that their vertices must be corresponding. Let's translate △ ADS so that ∠D and ∠H map onto each other.
From the diagram we see that â–³ A'D'S' and â–³ HFG are mirror images of each other. Therefore, if we reflect â–³ A'D'S in a vertical line of reflection through the lined up vertices D' and H, we can map the two triangles onto each other exactly.
