Question

PLZ HELP ASAP 15 POINTS!!!

The table shows the proof of the relationship between the slopes of two perpendicular lines. What is the missing statement in step 2? A.(AB/BC)=(CE/ED) B.(AB/CE)=(ED/BC) C.(AB/BC)=(ED/CE) D. (AB/CE)=(BE/ED)

Answer 1

A. (AB/BC)=(CE/ED)

Explanation:

Property of similar triangles :

If two triangles are similar then the corresponding sides are in same proportion,

Here,
`\triangle ABC\sim \triangle CED`

By the above property,

`(AB)/(BC)=(CE)/(ED)`

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.

Answer 2

A.(AB/BC)=(CE/ED)

Explanation:

Properties of Similar Triangles states two things

Corresponding angles are congruent (same measure)

Corresponding sides are all in the same proportion

That means AB/ BC = CE/ED