Question

Finish the Proof to prove that Triangle ACF is congruent to ECF. Multiple steps can be added.

Answer 1

We prove that,
`$\triangle A C F \cong \triangle E C F$` by using Angle-Side-Angle (ASA) congruence theorem.

The given diagram shows a triangle with a missing angle. The triangle is labeled
`\triangle A B C`, and the missing angle is
`$\angle C$`. The diagram also shows a line segment
`$\overline{E F}$` that intersects
`$\overline{A B}$` at point E and
`$\overline{B C}$` at point F.

To prove that
`$\triangle A C F \cong \triangle E C F$`, we can use the Angle-Side-Angle (ASA) congruence theorem. The ASA congruence theorem states that two triangles are congruent if they have two congruent angles and a congruent side between the angles.

In
`$\triangle A C F$` and
`$\triangle E C F$`, we have the following congruences:

-
`$\angle A C E \cong \angle E C F$` (given)

-
`$\angle A F C \cong \angle E F C$` (given)

- AC = EF (segments opposite congruent angles in a triangle are congruent)

Therefore, by the ASA congruence theorem, we can conclude that
`$\triangle A C F \cong \triangle E C F$`.