Answer:
See below.
Explanation:
We're asked to prove that ΔSTV ≅ ΔTUW.
Let's begin by reviewing what was given to us.
- Line Segment SV ≅ & ║ (Congruent and Parallel With) Line Segment TW.
- ∠SVT ≅∠TWU.
- SV ≅ TW.
Because we already have one side and an angle congruent, we need to prove that another angle or side is congruent.
Our goal is to find a Congruency Postulate to prove that ΔSTV ≅ ΔTUW.
As we can see in the diagram, ∠STV ≅ ∠UTV as they're vertical angles. This is possible because Line Segment SV ≅ & ║ Line Segment TW.
We are now able to prove that ΔSTV ≅ ΔTUW with the Angle-Side-Angle Triangle Congruency Postulate (ASA). We proved, and were given 2 angles, and 1 side.
Summary:
∠STV ≅ ∠UTV | Vertical Angles.
ΔSTV ≅ ΔTUW | ASA.