Question

write a proof of the triangle midsegment theorem. given: $overline{dg} cong overline{ge}$, $overline{fh} cong overline{he}$ prove: $overline{gh} parallel overline{df}$, $gh = \frac{1}{2}df$ find the ratios of the sides of $\triangle geh$ to $\triangle def$. what is $\frac{eg}{ed} = square$ (type an integer or a simplified fraction.) video textbook get more help

Explanation:

Step1: Identify segment length relation

Given $\overline{DG} \cong \overline{GE}$, so $EG = DG$. Thus, $ED = EG + DG = 2EG$.

Step2: Calculate the ratio

Substitute $ED = 2EG$ into the ratio $\frac{EG}{ED}$.
<Expression>
$\frac{EG}{ED} = \frac{EG}{2EG} = \frac{1}{2}$
</Expression>

Answer:

$\frac{1}{2}$