Question

Ethan is proving that the slope between any two points on a straight line is the same. He has already proved that triangles 1 and 2 are similar.

Drag statements and reasons to complete the proof.

Answer 1

Slope of a line = (y₂ - y₁)/(x₂ - x₁)

K'  = y₂ - y₁  ( for E & F)

L' = x₂ - x₁    ( for E & F)

=> Slope from E to F  = K'/L'

Two triangles are similar

=> K/K'  = L/L'  = DE/EF

=> K/K'  = L/L'

=> K/L = K'/L'

=>  K'/L' = K/L

Triangles are similar

K - L  = K' - L'

Sufficient information is not given but from picture it is clear that slope of line = 1

=> K = L    & K'  = L'

hence K - L = 0  & K' - L' = 0

=> K - L  = K' - L'

Answer 2

Answer:

Slope from P to Q = F/E ------ Definition of a Slope

Slope from Q to R = F1/E1 ------ Definition of a Slope

F1/ E1 = F/E ---------------- Triangle 1 is similar to triangle 2

Step-by-step explanation: