Questions: Complete the proof that TU VW.

Transcript text: Complete the proof that $T U \| V W$.

Solution

Step 1: Analyze the given information

We are given that UV is congruent to TW, VW is congruent to TU, and TV is congruent to itself. This sets us up to prove triangles congruent.

Step 2: Establish triangle congruence

Using the Side-Side-Side (SSS) postulate, we can prove that triangle TVW is congruent to triangle VTU.

Step 3: Identify corresponding angles

Because triangles TVW and VTU are congruent, their corresponding angles are congruent. This means angle TVW is congruent to angle UTV.

Step 4: Apply the converse of the alternate interior angles theorem

Since angles TVW and UTV are congruent alternate interior angles, lines TU and VW must be parallel.

Was this solution helpful?

Unhelpful

Helpful