Final answer:
In similar triangles, corresponding sides are proportional. So, if side DE is 3 units and ∆ABC and ∆DEF are similar triangles, the length of side EF would be a proportion of the length of side DE. The measure of ∠EDF would be 53° as corresponding angles in similar triangles are congruent.
Step-by-step explanation:
In similar triangles, corresponding sides are proportional. So, if side DE is 3 units and ∆ABC and ∆DEF are similar triangles, the length of side DE would be a proportion of the length of side EF. We can set up the following proportion:
DE/EF = AC/DF
Substituting the known values, we have: 3/EF = 3R/DF
Since AB = 3x, we have AB/DF = AC/DF = 3R/DF. Can you provide the value of R to calculate the length of side EF?
To find the measure of ∠EDF, we know that corresponding angles in similar triangles are congruent. Since ∠ABC is 53° and ∆ABC and ∆DEF are similar triangles, ∠EDF would also be 53°.