Question

1. ΔABC and ΔDEF are similar = Given
2. BC/EF = AB/DE = Property of Similar Triangles
3. AB/BC = EC/DE = Property of Proportion
4. Slope of AC = BC/AB = Definition of slope
5. Slope of DF = EF/DE = Definition of slope
6. ____________ = Substitution Property of Equality

The table contains the proof of the theorem of the relationship between slopes of parallel lines. What is the missing statement for step 6?

A. Slope of AC = -1/slope of DF
B. Slope of AC = 1/slope of DF
C. Slope of AC = -slope of DF
D. Slope of AC = slope of DF
E. Slope of AC = 1 -slope of DF

Answer 1

I think the answer is d. The slope of AC=Slope of DF.

Hope this helped☺☺

Answer 2

Answer:

Option D is correct

$\text{Slope of AC} = \text{Slope of DF}$

Step-by-step explanation:

Given:

1.

ΔABC and ΔDEF are similar

Property of similar states that corresponding sides are in proportion.

2.

$\frac{BC}{EF} = \frac{AB}{DE}$ [By property of similar triangles]

Property of proportions allows you to cross multiply the equation.

then;

3.

$\frac{AB}{BC} = \frac{DE}{EF}$   [Property of proportion]

Definition of slope: Slope is described as the steepness and direction of line.

then by definition of slope;

4.

$\text{Slope of AC} = \frac{BC}{AB}$

5.

$\text{Slope of DF} = \frac{EF}{DE}$

6.

Substitution property of equality states that:

If a = b then a can be substituted in place of b in any equation or vice-versa.

then;

$\text{Slope of AC} = \text{Slope of DF}$

Therefore, the missing step in 6 we get,

$\text{Slope of AC} = \text{Slope of DF}$