Question

(a) complete the congruence statement
$\angle e\cong$ $\angle l$
$\angle f\cong$ $\angle k$
$\angle g\cong$ $\angle j$
(b) find the following ratios.
write your answers as fractions in simplest form.
$\frac{lk}{ef} = \frac{1}{1}$
$\frac{kj}{fg} = \frac{1}{1}$
$\frac{lj}{eg} = \frac{1}{1}$
(c) select the true statement.
$\triangle efg$ and $\triangle lkj$ are similar.
$\triangle efg$ and $\triangle lkj$ are not similar.
be careful
write your answer in simplest form.
a denominator of 1 is not necessary.

Explanation:

Step1: Calculate \(\frac{LK}{EF}\)

Given \(LK = 20\) and \(EF = 16\), so \(\frac{LK}{EF}=\frac{20}{16}\). Simplify by dividing numerator and denominator by 4: \(\frac{20\div4}{16\div4}=\frac{5}{4}\).

Step2: Calculate \(\frac{KJ}{FG}\)

Given \(KJ = 40\) and \(FG = 32\), so \(\frac{KJ}{FG}=\frac{40}{32}\). Simplify by dividing numerator and denominator by 8: \(\frac{40\div8}{32\div8}=\frac{5}{4}\).

Step3: Calculate \(\frac{LJ}{EG}\)

Given \(LJ = 45\) and \(EG = 36\), so \(\frac{LJ}{EG}=\frac{45}{36}\). Simplify by dividing numerator and denominator by 9: \(\frac{45\div9}{36\div9}=\frac{5}{4}\).

Answer:

\(\frac{LK}{EF}=\boldsymbol{\frac{5}{4}}\), \(\frac{KJ}{FG}=\boldsymbol{\frac{5}{4}}\), \(\frac{LJ}{EG}=\boldsymbol{\frac{5}{4}}\)