Mathematics: What proportional segment lengths verify that bc∥de ? fill in the boxes to correctly complete the proportion. $$ = $$ a triangle with vertices labeled as a, b, c. side b c is base. sides a b and a c contain midpoints d and e, respectively. a line segment is drawn from d to e. side a d is labeled as 4. side d b is labeled as 6. side a e is labeled as 3.2. side e c is labeled as 4.8.

Its 3 and 4 i checked on class...

What proportional segment lengths verify that bc∥de

zackarygonzalez1028

06.01.2022

$\frac{4}{10}=\frac{3.2}{8.0}$

Step-by-step explanation:

Given,

ABC is a triangle,

In which, AD = 4 unit, DB = 6 unit, AE = 3.2 unit and EC = 4.8 unit,

⇒ $\frac{AD}{AB}=\frac{4}{4+6}=\frac{4}{10}=0.4$

$\frac{AE}{EC}=\frac{3.2}{3.2+4.8}=\frac{3.2}{8}=0.4$

$\implies \frac{AD}{AB}=\frac{AE}{EC}$

⇒ Δ ADE ≅ Δ ABC

⇒ ∠ADE ≅ ∠ABC and ∠AED ≅ ∠ACB

By the converse of alternate interior angle theorem.

BC ║ DE

Hence, the required proportion of segment is,

$\frac{4}{10}=\frac{3.2}{8.0}$

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