Question

Isosceles EFG is shown, where FA is an angle bisector. Drag statements and reasons to the table to complete the proof that the base angles of the isosceles triangle are congruent.

Statement 1: FG - EF and FA bisects CEFG.
Statement 2: GFH ≅ EFH
Statement 3:
Statement 4:
Statement 5: ∠EFG ≅ ∠EFH

Reason 1: Given
Reason 2: Definition of an angle bisector
Reason 3:
Reason 4:
Reason 5: Corresponding angles of congruent triangles are congruent.

a. Statement 3: FA ≅ EF; Reason 3: Transitive property
b. Statement 4: GFH ≅ AFH; Reason 4: Reflexive property
c. Statement 3: FA ≅ EF; Reason 3: Substitution
d. Statement 4: GFH ≅ AFH; Reason 4: SAS theorem

Answer 1

To prove that the base angles of the isosceles triangle EFG are congruent, we use the properties of an angle bisector and the corresponding angles of congruent triangles.

Step-by-step explanation:

To prove that the base angles of the isosceles triangle EFG are congruent:

1. Statement 1: FG = EF and FA bisects ∠CEFG. (Given)
2. Statement 2: ∠GFH is congruent to ∠EFH. (Definition of an angle bisector)
3. Statement 3: FA ≅ EF. (Substitution)
4. Reason 1: ∠EFG is congruent to ∠EFH. (Corresponding angles of congruent triangles are congruent)

Therefore, the base angles ∠EFG and ∠EFH of the isosceles triangle EFG are congruent.