Question

which two triangles below could lie on the same graphed line? explain. (triangles not drawn to scale.) a 13 b 18 20 c 45 50 a&c a&b b&c none

Explanation:

Step1: Calculate slope - like ratios

For right - angled triangles on a line, the ratio of the vertical side to the horizontal side (similar to slope) should be equal. For triangle A, assume the horizontal side is \(x_1\) and vertical is \(y_1 = 13\), for triangle B horizontal is \(x_2\) and vertical \(y_2=20\), for triangle C horizontal is \(x_3\) and vertical \(y_3 = 50\). Let's find the ratios of vertical to horizontal sides. For triangle B, if we assume the ratio of vertical to horizontal is \(r_1=\frac{20}{18}=\frac{10}{9}\), for triangle C, \(r_2=\frac{50}{45}=\frac{10}{9}\).

Step2: Compare ratios

Since the ratios of the vertical side to the horizontal side of triangle B and triangle C are equal (\(\frac{20}{18}=\frac{50}{45}\)), they could lie on the same graphed line.

Answer:

C. B&C