Given that the triangles, ABC and DEF are similar to each other, applying the theorem of similar triangles, the length of:
a. Segment DF = 2.68
b. Segment EF = 2.01
Recall the following about Triangles that are similar:
- Similar triangles have side lengths that are proportional to each other.
- The ratio of their corresponding three side lengths are the same.
Thus:
Given that [tex]\triangle[/tex]ABC and [tex]\triangle[/tex]DEF are similar, therefore:
AB/DE = BC/EF = AC/DF
Length of Segment DF:
Using AB/DE = AC/DF,
AB = 2
AC = 4
DE = 1.34
DF = ?
[tex]\frac{2}{1.34} = \frac{4}{DF}[/tex]
- Cross multiply and solve for DF
[tex]\frac{2}{1.34} = \frac{4}{DF}\\\\DF = \frac{4 \times 1.34}{2} \\\\\mathbf{DF = 2.68}[/tex]
Length of Segment EF:
Using AB/DE = BC/EF,
AB = 2
BC = 3
DE = 1.34
EF = ?
[tex]\frac{2}{1.34} = \frac{3}{EF}[/tex]
- Cross multiply and solve for EF
[tex]\frac{2}{1.34} = \frac{3}{EF}\\\\EF = \frac{3 \times 1.34}{2} \\\\\mathbf{EF = 2.01}[/tex]
Therefore, given that the triangles, ABC and DEF are similar to each other, applying the theorem of similar triangles, the length of:
a. Segment DF = 2.68
b. Segment EF = 2.01
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