Question

Geometry help please! Match the reasons with the statements.

Answer 1

Given:

∠PRS and ∠VUW are supplementary.

To prove:

Line TV || Line QS

Solution:

Step 1: Given

∠PRS and ∠VUW are supplementary.

Step 2: By the definition of supplementary angles

$m\angle {PRS}+m\angle {VUW}=180^{\circ}$

Step 3: Angles forming a linear pair sum to 180°

$m\angle {PRS}+m\angle {SRU}=180^{\circ}$

Step 4: By transitive property of equality

step 2 = step 3

$m\angle {PRS}+m\angle {VUW}=m\angle {PRS}+m\angle {SRU}$

Step 5: By algebra cancel the common terms in both side.

${m} \angle {VUW}={m} \angle{SRU}$

Step 6: By converse of corresponding angles postulate

Line TV || Line QS

Hence proved.