Question

Geometry help please! Match the reasons with the statements.

Answer 1

• Given ⇔ 1. ∠PRS and ∠VUW are supplementary
• Angles forming a linear pair sum of 180° ⇔ 3. ∠PRS + ∠SRU = 180°
• Definition of Supplementary angle ⇔ 2. ∠PRS + ∠VUW = 180°
• Transitive property of equality ⇔ 4 . ∠PRS + ∠VUW = ∠PRS + ∠SRU
• Algebra ⇔ 5. ∠VUW = ∠SRU
• Converse of Corresponding angle Postulate ⇔ Line TV || Line QS

Explanation:

Here we have , ∠PRS and ∠VUW are supplementary . We need to complete the proof of TV || QS , with matching the reasons with statements .Let's do this :

• Given ⇔ 1. ∠PRS and ∠VUW are supplementary
• Angles forming a linear pair sum of 180° ⇔ 3. ∠PRS + ∠SRU = 180°
• Definition of Supplementary angle ⇔ 2. ∠PRS + ∠VUW = 180°
• Transitive property of equality ⇔ 4 . ∠PRS + ∠VUW = ∠PRS + ∠SRU
• Algebra ⇔ 5. ∠VUW = ∠SRU
• Converse of Corresponding angle Postulate ⇔ Line TV || Line QS

Above mentioned are , are the statements matched with expressions on right hand side (RHS) .

• The Corresponding Angles Postulate states that, when two parallel lines are cut by a transversal , the resulting corresponding angles are congruent .

• The converse states: If corresponding angles are congruent, then the lines cut by the transversal are parallel.