Question

1. prove that △abc ~ △def using the sss similarity criterion, where ab = 6, bc = 8, ac = 10, de = 9, ef = 12, and df = 15. fill in the missing ratio.

statement
\\( \frac { a b } { d e } = \frac { 6 } { 9 } = \frac { 2 } { 3 } \\)
\\( \frac { b c } { e f } = \frac { 8 } { 12 } = \frac { 2 } { 3 } \\)
\\( \frac { a c } { d f } = \\)
\\( \frac { a b } { d e } = \frac { b c } { e f } = \frac { a c } { d f } \\)
△abc ~ △def
reason
given side lengths
given side lengths
given side lengths
ratios of corresponding sides are equal
sss similarity criterion

Explanation:

Step1: Calculate the ratio of \( \frac{AC}{DF} \)

Given \( AC = 10 \) and \( DF = 15 \).

$$ \frac{AC}{DF}=\frac{10}{15}=\frac{2}{3} $$

Answer:

\(\frac{2}{3}\)