Answer:
Side DF = 4 units
Step-by-step explanation:
Similar triangles states that the triangles with equal corresponding angles and proportionate sides.
Given: ΔABC and ΔDEF are similar
Corresponding angles are;
[tex]\angle A = \angle D[/tex] ,
[tex]\angle B = \angle C[/tex] ,
[tex]\angle C= \angle F[/tex]
Proportionate sides are;
[tex]\frac{AB}{DE} =\frac{BC}{EF} =\frac{AC}{DF}[/tex]
It is also given BC = 6 units , EF = 8 units and DF -AC = 1
Let AC = x units then;
DF = x +1 units.
Then, by definition of similar triangle ;
[tex]\frac{BC}{EF} =\frac{AC}{DF}[/tex]
[tex]\frac{6}{8} =\frac{x}{x+1}[/tex]
By cross multiply we have;
[tex]6(x+1) = 8x[/tex]
Using distributive property; [tex]a\cdot(b+c) = a\cdot b+ a\cdot c[/tex]
6x + 6 = 8x
Subtract 6x on both sides we get;
6x + 6 -6x = 8x -6x
Simplify:
6 = 2x
Divide by 2 on both sides we get;
x = 3
DF = x +1 = 3+1 = 4
Therefore, the side DF is, 4 units
