Question

∠t ≅ ∠vux and →{tw} || →{uv}. complete the proof that ∠w ≅ ∠uvx.

1 ∠t ≅ ∠vux given
2 →{tw} || →{uv} given
3 ∠t ≅ ∠uvx
4 ∠vux ≅ ∠w
5 ∠t ≅ ∠w
6 ∠w ≅ ∠uvx transitive property of congruence

Explanation:

Step1: Alternate - interior angles

Since \(\overleftrightarrow{TW}\parallel\overleftrightarrow{UV}\), by the Alternate - interior angles theorem, \(\angle T\cong\angle UVX\).

Step2: Alternate - interior angles

Since \(\overleftrightarrow{TW}\parallel\overleftrightarrow{UV}\), by the Alternate - interior angles theorem, \(\angle VUX\cong\angle W\).

Step3: Transitive property

Since \(\angle T\cong\angle VUX\) (given) and \(\angle VUX\cong\angle W\), by the Transitive property of congruence, \(\angle T\cong\angle W\).

Answer:

1. Alternate - interior angles theorem; 4. Alternate - interior angles theorem; 5. Transitive property of congruence.