Question

if ∠8≅∠10 and ∠1≅∠7, which describes all the lines that must be parallel? only lines r and s must be parallel. only lines t and u must be parallel. lines r and s and lines t and u must be parallel. neither lines r and s nor lines t and u must be parallel.

Explanation:

Step1: Recall corresponding - angle postulate

If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

Step2: Analyze ∠8 and ∠10

∠8 and ∠10 are corresponding angles formed by lines r and s cut by transversal u. Since ∠8≅∠10, by the corresponding - angle postulate, lines r and s are parallel.

Step3: Analyze ∠1 and ∠7

∠1 and ∠7 are corresponding angles formed by lines t and u cut by transversal r. Since ∠1≅∠7, by the corresponding - angle postulate, lines t and u are parallel.

Answer:

C. Lines r and s and lines t and u must be parallel.