Question

1. the graph of line u is shown. use the similar slope triangles to compare the slopes of segments gi and ik. (example 3)

Explanation:

Step1: Recall Slope Formula

The slope of a line segment between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For similar slope triangles, the ratios of rise over run should be equal.

Step2: Analyze Triangles for \(GI\) and \(IK\)

• For segment \(GI\), consider the triangle \(GHI\). Let the rise (vertical change) be \(h_1\) and run (horizontal change) be \(w_1\).
• For segment \(IK\), consider the triangle \(IKJ\) (or the larger triangle with \(K\) on the x - axis). Let the rise be \(h_2\) and run be \(w_2\).
• Since the triangles are similar (as per the problem statement, using similar slope triangles), the ratio \(\frac{h_1}{w_1}=\frac{h_2}{w_2}\). This means that the slope of \(GI\) (which is \(\frac{h_1}{w_1}\)) and the slope of \(IK\) (which is \(\frac{h_2}{w_2}\)) are equal. Because similar triangles have proportional corresponding sides, so the ratio of rise to run (slope) for both segments is the same.

Answer:

The slopes of segments \(GI\) and \(IK\) are equal.