Question

Copy everything shown. Complete the proof.

Given:$\angle \mathbf{2}\cong \angle \mathbf{3}$

Prove: $\mathbf{\angle }\mathbf{1}\mathbf{\cong }\mathbf{\angle }\mathbf{4}$

Proof:

Short answer

statements	Reasons
1.$\angle 1\cong \angle 2$	1. vertical angles
2.$\angle 2\cong \angle 3$	2. Given
3.$\angle 3\cong \angle 4$	3. vertical angles
4.$\angle \mathbf{1}\cong \angle \mathbf{4}$	4. Transitive property (used twice)

Step-by-step solution

Step 1. Write the relation between the angles ∠1 and ∠2.

From the given diagram it can be noticed that the angles$\angle 1$ and$\angle 2$ are vertical angles, therefore the angles$\angle 1$ and$\angle 2$ are congruent angles.

Step 2. Write the relation between the angles ∠2 and ∠3.

The angles$\angle 2$ and$\angle 3$ are congruent angles as it is given that $\angle 2\cong \angle 3$.

Step 3. Write the relation between the angles ∠3 and ∠4.

From the given diagram it can be noticed that the angles$\angle 3$ and$\angle 4$ are vertical angles, therefore the angles$\angle 3$ and$\angle 4$ are congruent angles.

Step 4. write the relation between the angles ∠1 and ∠4.

The angles$\angle 1$ and$\angle 4$ are congruent angles by using the transitive property twice.