Answer: Option first Slope of AC×Slope of DC = -EC/DE×DE/EC is the missing statement in step 6.
Explanation:
Here, we have two triangles[tex]\triangle ABC[/tex] and [tex]\triangle CDE[/tex] which are similar to each other. And, [tex]AC\perp CD[/tex]
Since, if two triangles are similar then their corresponding ratios of sides are equal.
Therefore, [tex]\frac{AB}{EC} =\frac{BC}{DE}[/tex]
⇒ [tex]\frac{AB}{BC} =\frac{EC}{DE}[/tex] ---------(1)
Now, by the definition of slope, slope of [tex]AC= -\frac{AB}{BC}[/tex]------(2)
Similarly, Slope of [tex]DC=\frac{DE}{AC}[/tex] -------(3)
On multiplying equation (2) and (3),
slope of AC[tex]\times[/tex] Slope of DC=[tex]-\frac{AB}{BC}\times \frac{DE}{AC}[/tex]
⇒slope of AC[tex]\times[/tex] Slope of DC= [tex]-\frac{EC}{DE} \times \frac{DE}{EC}[/tex] (From equation (1))
slope of AC[tex]\times[/tex] Slope of DC=-1 (Simplifying the right side)
