Question

Given that △ABC with AB ≅ AC, draw segment BD through the midpoint F of AC such that BF ≅ DF. Prove that △AFB ≅ △CFD

Answer 1

To prove that triangle AFB is congruent to triangle CFD, we use the SAS postulate, as they share two equal sides and an included angle due to the given conditions of AB ≅ AC and midpoint F.

Step-by-step explanation:

You want to prove that triangle AFB is congruent to triangle CFD. Since AB ≅ AC (given) and segment BD intersects AC at its midpoint F, we have A F = FC and BF = DF (given). Now we have two triangles A FB and CFD where:

• A F = FC
• BF = DF
• Angle AFB = angle CFD (vertical angles are equal).

By the SAS (Side-Angle-Side) postulate, since two sides and the included angle in triangle AFB are equal to two sides and the included angle in triangle CFD, the two triangles are congruent.