Answer: ΔABC, ΔDEF and ΔGHI are similar to one another.
Step-by-step explanation: We are given four triangles on the coordinate plane and we to check which can be mapped to one another by similarity transformation.
We have
In ΔABC, AC = 12 units, BC = AB = 6√2 units.
In ΔDEF, DF = 8 units, DE = EF = 4√2 units.
In ΔPQR, PR = 14 units, PQ = 10 units, QR = 6√2 units.
In ΔGHI, GH = 32 units, GI = IH = 16√2 units.
We can see that triangles ABC, DEF and GHI are isosceles but ΔPQR is not isosceles, so it cannot be similar to the others.
Also,
[tex]\dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{CA}{DF}=\dfrac{3}{2},[/tex]
and
[tex]\dfrac{AB}{IH}=\dfrac{BC}{GI}=\dfrac{CA}{GH}=\dfrac{3}{8},[/tex]
Therefore, ΔABC similar to ΔDEF and ΔABC similar to ΔGHI.
Therefore, ΔABC, ΔDEF and ΔGHI are similar to one another.
