How many triangles in the diagram can be mapped to one another by similarity transformation?

the answer is 3

Step-by-step explanation:

 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,

and

Therefore, ΔABC similar to ΔDEF and ΔABC similar to ΔGHI.

Therefore, ΔABC, ΔDEF and ΔGHI are similar to one another.

ddd

step-by-step explanation:

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