Question

What is the relationship between the slope of the line and the side lengths of the triangles? ​

Answer 1

For the smaller triangle, the rise is 2 since this is the length of the vertical component. The horizontal component is 3, meaning the run is 3

Slope = rise/run

Slope = 2/3

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The larger triangle leads to the same slope because

slope = rise/run

slope = 4/6

slope = (2*2)/(2*3)

slope = 2/3

Because we get the same slope value, this confirms that both triangles have their hypotenuse on the same straight line.

The two triangles are similar. The larger triangle's sides are twice as long as its smaller counterpart.