Question

Please help:

Given: ∠4 is congruent to ∠2
Prove: ∠3 and ∠1 are supplementary

Statements and Reasons

Answer 1

See Below.

Explanation:

We can write a two-column proof.

Statements: Reasons:

`\displaystyle 1)\, \angle 4\cong \angle 2` Given

`\displaystyle 2)\, \angle 3 \cong \angle 4` Vertical Angles are Congruent

`\displaystyle 3) \, \angle 1 + \angle 2 = 180` Linear Pair

`\displaystyle 4)\, \angle 1 + \angle 4 = 180` Substitution

`\displaystyle 5) \, \angle 1 + \angle 3 = 180` Substitution

`\displaystyle 6) \, \text{$\angle 3$ and $\angle 1$ are supplementary}` Definition of Supplementary Angles