Given: �ÚA ≅�ÚE

CF bisects �ÚECA
Prove: �¢AFB≅ �¢EFD

no idea where B and D are. Please explain the diagram, which does not appear here.

美丽世界私服一条龙_乱勇OL私服一条龙_倚天2私服一条龙_完美世界私服一条龙_征服私服一条龙魔兽sf一条龙41ay.comQQ30171491

To prove that triangles �¢AFB and �¢EFD are congruent, we can use the information given and apply several congruence criteria.

Given statements:
1. �ÚA ≅ �ÚE (Triangle A is congruent to Triangle E)
2. CF bisects �ÚECA (CF is a bisector of angle ECA)

We need to prove that �¢AFB ≅ �¢EFD.

Proof:

Step 1: Given that �ÚA ≅ �ÚE, we know that side AF is congruent to side EF.
(AF ≅ EF)

Step 2: We are also given that CF bisects angle ECA.
Therefore: Angle ECF is congruent to angle FCA.
(angle ECF �≅ angle FCA)

Step 3: We can use the Angle-Bisector Theorem, which states that if a line bisects an angle, it divides the opposite side into segments that have the same ratio as the other two sides of the triangle.
Since CF bisects angle ECA, it divides side AE and side AC in the same ratio as side EF and side FC.

As a result, we can say that:
Segment AE/Segment EC = Segment EF/ Segment FC.
(AE/EC = EF/FC)

Step 4: Combining step 1 and step 3, we can conclude that side AF/ side CF = side EF/side FC.
(AF/CF = EF/FC)

Step 5: By the Side-Angle-Side (SAS) congruence criterion, we can now prove that triangles �¢AFB and �¢EFD are congruent.
AF ≅ EF (from step 1)
angle AFB ≅ angle EFD (since angle AFB and angle EFD are vertical angles)
AF/CF = EF/FC (from step 4)

Therefore, by SAS, triangle �¢AFB is congruent to triangle �¢EFD.
(�¢AFB ≅ �¢EFD)

Hence, we have proven that triangles �¢AFB and �¢EFD are congruent.