Answer:
The true equations are,
CA/C'A' = CB/C'B'
and,
A'B'/AB=C'B'/CB
Explanation:
Since we use a dilation, the length A'B' is not equal to AB and so on for the other lengths,
Since A'C' is not equal to AC (due to the dilation)
hence A'C'/BA does not equal AC/BA
hence the first option is false
B'C'/B'A' = BA/BC is false because a/b does not necessarily equal b/a (for example 3/4 is not equal to 4/3)
AC/A'C' = B'A'/BA ,collecting all terms of the same triangle on one side, we get,
1/(A'C')(B'A') = 1/(AC)(BA) but since A'C' = AC is false (due to dilation)
so, 1/(A'C')(B'A') = 1/(AC)(BA) is also false and AC/A'C' = B'A'/BA is also false
CA/C'A' = CB/C'B'
Collecting terms from the same triangle on either side, we get,
C'B'/C'A' = CB/CA
Now, since the ratios of the lengths do not change in a dilation, this relation is true
A'B'/AB=C'B'/CB
Collecting terms from the same triangle on either side, we get,
A'B'/C'B' = AB/CB
Now, since the ratios of the lengths do not change in a dilation, this relation is true