Answer:
A. (AB/BC)=(CE/ED)
Step-by-step explanation:
Property of similar triangles :
If two triangles are similar then the corresponding sides are in same proportion,
Here, [tex]\triangle ABC\sim \triangle CED[/tex]
By the above property,
[tex]\frac{AB}{BC}=\frac{CE}{ED}[/tex]
Hence, the column prove would be,
Statements Reason
1. AC ⊥ CD
Δ ABC is similar to ΔCED Given
2. (AB/BC)=(CE/ED) Property of similar triangle
3. Slope of AC = -AB/BC Definition of slope
Slope of CD = ED/CE
4. Slope of AC × Slope of CD Multiplying the slopes
= -AB/BC × ED/CE
5. Slope of AC × Slope of CD Substitution property of equality
= -CE/ED × ED/CE
6. Slope of AC × Slope of CD = -1 Simplifying the right side.
Hence, option 'A' is correct.
