Question

The table shows the proof of the relationship between the slopes of two perpendicular lines. What is the missing statement in step 6?
A) slope of AC x slope of DC= EC/DC x DC/EC

B) slope of AC x -slope of DC=1

C) slope of AC x slope of DC=1

D) slope of AC x slope of DC=-EC/DC x DC/EC


Statement

1. AC←→⊥CD←→ (view diagram) ΔABC is similar to ΔCED.

2. (This statement is intentionally left blank.)

3. ABBC = ECDE

4. slope of AC←→ = -ABBC slope of DC←→ = DEAC

5. slope of AC←→ × slope of DC←→ = -ABBC×DEEC

6. ?

7. slope of AC←→ × slope of DC←→ = -1 simplifying the right side

Reason

1. given

2. property of similar triangles

3. property of proportion

4. definition of slope

5. multiplying the slopes

6. Substitution Property of Equality

7. simplifying the right side

Answer 1

We have here an outline for the proof. Up to step 5, we have used only similarity of triangles and extracted some information on them. Now, we can substitute equation 3 in order to calculate the value of the product of slopes from AC and DC. Hence, the correct choice is where this substitution is shown, hence choice D. We could have trimmed down our choices by noticing that A and C are factually incorrect (-1, not 1)

Answer 2

The answer is AB/BC = EC/DE