Question

Fill in the missing statements and reasons to prove that

Answer 1

The two column proof has shown that ∠DFG and ∠DEF are supplementary

How to prove the angles?

The two column proof to show that ∠DFG and ∠DEF are supplementary are as follows:

Statement 1: ∠DFE ≅ ∠DEF → m∠DFE ≅ m∠DEF

Reason 1: Base angles of an Isosceles triangle are congruent

Statement 2: ∠DFG and ∠DFE are supplementary → m∠DFG + m∠DFE = 180°

Reason 2: Definition of supplementary angles

Statement 3: m∠DFG + m∠DEF = 180°

Reason 3: Substitution

Statement 4: ∠DFG + ∠DEF = 180°

Reason 4: ∠DFG and ∠DEF are supplementary