Question

Given: ∠T ≅ ∠V; ST || UV
Prove: TU || VW

4 connected lines are shown. A line from point S goes slightly down and to the left to point T to form S T. A line from point T goes slightly down and to the right to point U to form T U. A line from point U goes slightly down and to the left to point V to form U T. A line goes slightly down and to the right to point W to form point W.

Complete the two-column proof.

♣ =

♦ =

♠ =

Answer 1

Here is a short two-column proof and the meanings of the symbols.

Two-column proof

Statements
1. ∠T ≅ ∠V
2. ST || UV
3. ∠STU and ∠UVW are corresponding angles
4. TU || VW

Reasons
1. Given
2. Given
3. If two lines are parallel, then corresponding angles formed by transversals are congruent (so ∠STU corresponds to ∠UVW)
4. If corresponding angles are congruent, then the lines (the transversals) are parallel (converse of the corresponding-angles theorem)

Therefore TU || VW.

Answers to the blanks
♣ = Given
♦ = Given
♠ = If corresponding angles are congruent, then the lines are parallel (converse of the corresponding-angles theorem)