Guided Example #1 - Parallelism and Euclidean Geometry

In the figure, point B is between points A and C, and point E is between points D and F.

Given that $\bar{A B} ≅ \bar{D E}$ and $\bar{B C} ≅ \bar{E F}$ , prove that $\bar{A C} ≅ \bar{D F}$ .

Statement

Reason

point B is between A and C
point E is between D and F

$\bar{A B} ≅ \bar{D E}$

Given

Statement

Reason

point B is between A and C
point E is between D and F

$\bar{A B} ≅ \bar{D E}$

Given

AB + BC = DE + EF

Addition postulate

Statement	Reason
point B is between A and C point E is between D and F $\bar{A B} ≅ \bar{D E}$	Given
AB + BC = DE + EF	Addition postulate
So AC = DF	Point Between postulate

Statement	Reason
point B is between A and C point E is between D and F $\bar{A B} ≅ \bar{D E}$	Given
AB + BC = DE + EF	Addition postulate
So AC = DF	Point Between postulate
=> $\bar{A C} ≅ \bar{D F}$