Question

use similar slope triangles to compare the slope of segment ac and ce
similar triangles and slope

Explanation:

Step1: Recall slope - formula

The slope $m$ of a line segment with two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For similar slope - triangles, the ratio of the vertical change (rise) to the horizontal change (run) is the same.

Step2: Analyze triangle for AC

Suppose the coordinates of point A are $(x_A,y_A)$ and of point C are $(x_C,y_C)$. If we assume A is at $(2,2)$ and C is at $(8,6)$. Then the slope of AC, $m_{AC}=\frac{y_C - y_A}{x_C - x_A}=\frac{6 - 2}{8 - 2}=\frac{4}{6}=\frac{2}{3}$.

Step3: Analyze triangle for CE

Suppose the coordinates of point C are $(x_C,y_C)$ and of point E are $(x_E,y_E)$. If C is at $(8,6)$ and E is at $(14,10)$. Then the slope of CE, $m_{CE}=\frac{y_E - y_C}{x_E - x_C}=\frac{10 - 6}{14 - 8}=\frac{4}{6}=\frac{2}{3}$.
Since the two triangles are similar, the ratios of their vertical to horizontal sides are equal, so the slopes of AC and CE are equal and equal to $\frac{2}{3}$.

Answer:

The slope of segment AC and CE is the same, and the slope value is $\frac{2}{3}$.