Question

for each pair of triangles, write a proportion that shows that the ratios of the base, b, to the height, h, are the same. use the cross - products rule to check.
5.
60 m
40 m
24 m
36 m
6.
12 cm
5 cm
7.5 cm
18 cm

Explanation:

Step1: For the first pair of triangles

Let the first triangle have base $b_1 = 60$ m and height $h_1=40$ m, the second triangle have base $b_2 = 36$ m and height $h_2 = 24$ m. The proportion is $\frac{b_1}{h_1}=\frac{b_2}{h_2}$.

Step2: Calculate the ratios

For the first - triangle, $\frac{b_1}{h_1}=\frac{60}{40}=\frac{3}{2}$. For the second - triangle, $\frac{b_2}{h_2}=\frac{36}{24}=\frac{3}{2}$. The proportion is $60:40 = 36:24$.

Step3: For the second pair of triangles

Let the first triangle have base $b_3 = 12$ cm and height $h_3 = 5$ cm, the second triangle have base $b_4=18$ cm and height $h_4 = 7.5$ cm. The proportion is $\frac{b_3}{h_3}=\frac{b_4}{h_4}$.

Step4: Calculate the ratios

For the first - triangle, $\frac{b_3}{h_3}=\frac{12}{5}$. For the second - triangle, $\frac{b_4}{h_4}=\frac{18}{7.5}=\frac{18\times2}{7.5\times2}=\frac{36}{15}=\frac{12}{5}$. The proportion is $12:5 = 18:7.5$.

Answer:

For the first pair of triangles: $60:40 = 36:24$; For the second pair of triangles: $12:5 = 18:7.5$