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$Given 5. that /_\ABC~=/_\DEF. If m bar(AB)=2x+5, m bar(DE)=3(6+y), m bar(EF)=1+y and m bar(BC)=3y-x what is the lenght of bar(mEF) ?$

Given $\newline$ $5$ . that $\triangle A B C \cong \triangle D E F$ . If $m \overline{A B}=2 x+5$ , $m \overline{D E}=3(6+y)$ , $m \overline{E F}=1+y$ and $m \overline{B C}=3 y-x$ what is the lenght of $\overline{m E F}$ ?

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Csc, sec, and cot of special angles

Full solution

Q. Given

\newline

5

. that

\triangle A B C \cong \triangle D E F

. If

m \overline{A B}=2 x+5

,

m \overline{D E}=3(6+y)

,

m \overline{E F}=1+y

and

m \overline{B C}=3 y-x

what is the lenght of

\overline{m E F}

?

Equating Corresponding Sides: Since triangles $ABC$ and $DEF$ are similar, corresponding sides are proportional. We equate the expressions for corresponding sides $AB$ and $DE$ .
Finding y Value: We already know the expression for EF, which is $m \overline{EF} = 1 + y$ . To find $y$ , we solve the equation from the previous step.
Setting up Proportionality Equation: We use the proportionality of sides $BC$ and $EF$ . Set up the equation for $BC$ and $EF$ .
Solving System of Equations: Now we have a system of equations: $\newline$ $1$ . $2x - 3y = 13$ $\newline$ $2$ . $2y - x = 1$ $\newline$ We solve this system by substitution or elimination.
Substituting y into EF Expression: Substitute $y = 15$ back into the expression for $m \overline{EF}$ .

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