Question

Outline the necessary transformations to prove CBF ≅ EDF using a paragraph proof. Be sure to name specific sides or angles used in the transformation and any congruency statements.

Answer 1

See explanation.

Explanation:

Given:
`\overline{CB}\parallel \overline {ED}`

Consider triangles CBF and EDF. In these triangles,

• 
  `\overline {CB}\cong \overline{ED}` - given;

• 
  `\angle FCB\cong \angle FED` - as alternate interior angles when two parallel lines CB and ED are cut by transversal CE;

• 
  `\angle FBC\cong \angle FDE` - as alternate interior angles when two parallel lines CB and ED are cut by transversal BD.

By ASA postulate, triangles CBF and EDF are congruent.