please help me with this im struggling

AB and DE correspond to each other. The segments are composed of the 1st and 2nd points.
BC and EF correspond as well. The segments use the 2nd and 3rd points.
AC and DF correspond also. They use the 1st and 3rd points.

We want to find how long EF is, which means we'll involve BC = 17 since it is paired with it.

The diagram shows that AC = 14 and DF = 3, which is another pair we'll use

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The key takeaway is that

AC = 14 and DF = 3 pair up together
BC = 17 and EF also pair up together

Those two facts lead to the steps below

[tex]\frac{AC}{DF} = \frac{BC}{EF}\\\\\frac{14}{3} = \frac{17}{EF}\\\\14*EF = 3*17\\\\14*EF = 51\\\\EF = \frac{51}{14}\\\\EF \approx 3.642857\\\\EF \approx 3.6\\\\[/tex]

The proportion in step 1 is valid due to the similar triangles, and because of the corresponding side pairs mentioned. In step 3, I cross multiplied.

semsee45 semsee45 · Answer 2 · 2022-07-19T16:11:38+02:00

Answer:

3.6 cm

Step-by-step explanation:

Similar Triangle Theorem

If two triangles are similar, the ratio of their corresponding sides is equal.

Given triangles:

ΔABC and ΔDEF

Therefore the corresponding sides are:

AC and DF, BC and EF, AB and DE

To find the measure of side EF, use the Similar Triangle Theorem:

[tex]\implies \sf AC:DF=BC:EF[/tex]

[tex]\implies \sf \dfrac{AC}{DF}=\dfrac{BC}{EF}[/tex]

[tex]\implies \sf \dfrac{14}{3}=\dfrac{17}{EF}[/tex]

[tex]\implies \sf EF=17 \cdot \dfrac{3}{14}[/tex]

[tex]\implies \sf EF=\dfrac{51}{14}[/tex]

[tex]\implies \sf EF=3.642857...[/tex]

[tex]\implies \sf EF=3.6\:cm\:\:(nearest\:tenth)[/tex]

Learn more about similar triangles here:

https://brainly.com/question/26226516