To explain: what can be said about the lines PQ― and RS―, it is given that ∠1=∼∠2 and ∠4=∼∠5. Given: The diagram:

Question

To explain: what can be said about the lines PQ― and RS―, it is given that ∠1=∼∠2 and ∠4=∼∠5.  Given:  The diagram:

SoosteethicU · Accepted Answer

Concept Used: Theorem 2-3: Vertically opposite angles are congruent. Transitive property of congruence: if a=∼b and b=∼c, then a=∼c. Theorem 3-5: If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. Consider the given figure:  In this figure, by theorem 2-3, ∠2=∼∠5 (Vertically opposite angles) Also, it is given that, ∠1=∼∠2 and ∠4=∼∠5 Now applying the transitive property of congruence, it can be said that ∠1=∼∠4 From the above figure, it can be observed that the angles ∠1 and ∠4 are the alternate interior angles which are formed when the lines PQ― and RS― are cut by the transversal QR―. And since ∠1=∼∠4, so by the theorem 3-5, it can be said that the lines PQ― and RS― are parallel.

To explain: what can be said about the lines \overline{PQ}\ and\ \overline{RS}

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