Answer:
Option D is correct
[tex]Slope[/tex] [tex]of[/tex] [tex]AC=Slope[/tex] [tex]of[/tex] [tex]DF[/tex]
Step-by-step explanation:
Given:
1.
ΔABC and ΔDEF are similar
Property of similar states that corresponding sides are in proportion.
2.
[tex]\frac{BC}{EF}=\frac{AB}{DE}[/tex] [By property of similar triangles]
Property of proportions allows you to cross multiply the equation.
then;
3.
[tex]\frac{AB}{BC}=\frac{DE}{EF}[/tex] [Property of proportion]
Definition of slope: Slope is described as the steepness and direction of line.
then by definition of slope;
4.
[tex]Slope[/tex] [tex]of[/tex] [tex]AC=\frac{BC}{AB}[/tex]
5.
[tex]Slope[/tex] [tex]of[/tex] [tex]DF=\frac{EF}{DE}[/tex]
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;
[tex]Slope[/tex] [tex]of[/tex] [tex]AC= Slope[/tex] [tex]of[/tex] [tex]DF[/tex]
Therefore, the missing step in 6 we get,
[tex]Slope[/tex] [tex]of[/tex] [tex]AC= Slope[/tex] [tex]of[/tex] [tex]DF[/tex]
