Question

(a) complete the congruence statements below.
∠b≅ ∠l
∠c≅ ∠m
∠d≅ ∠k
(b) find the following ratios.
write your answers as fractions in simplest form.
\\(\frac{km}{bc} = \square\\) \\(\frac{ml}{cd} = \square\\) \\(\frac{kl}{bd} = \square\\)
(c) select the true statement.
○ △bcd and △kml are similar.
○ △bcd and △kml are not similar.

Explanation:

Step1: Calculate $\frac{KM}{BC}$

Given $KM = 49$ and $BC = 28$. So, $\frac{KM}{BC}=\frac{49}{28}$. Simplify by dividing numerator and denominator by 7: $\frac{49\div7}{28\div7}=\frac{7}{4}$.

Step2: Calculate $\frac{ML}{CD}$

Given $ML = 63$ and $CD = 36$. So, $\frac{ML}{CD}=\frac{63}{36}$. Simplify by dividing numerator and denominator by 9: $\frac{63\div9}{36\div9}=\frac{7}{4}$.

Step3: Calculate $\frac{KL}{BD}$

Given $KL = 28$ and $BD = 16$. So, $\frac{KL}{BD}=\frac{28}{16}$. Simplify by dividing numerator and denominator by 4: $\frac{28\div4}{16\div4}=\frac{7}{4}$.

Answer:

$\frac{KM}{BC}=\frac{7}{4}$, $\frac{ML}{CD}=\frac{7}{4}$, $\frac{KL}{BD}=\frac{7}{4}$