Question

8 given: r || s, s || t prove: ∠6 ≅ ∠7

Explanation:

Step1: Given

\(r\parallel s\)

Step2: Corresponding angles

\(\angle6\cong\angle10\) (If two parallel lines are cut by a transversal, then corresponding angles are congruent)

Step3: Given

\(s\parallel t\)

Step4: Alternate interior angles

\(\angle10\cong\angle7\) (If two parallel lines are cut by a transversal, then alternate interior angles are congruent)

Step5: Transitive property

\(\angle6\cong\angle7\) (If \(\angle A\cong\angle B\) and \(\angle B\cong\angle C\), then \(\angle A\cong\angle C\))

Answer:

\(\angle6\cong\angle7\) is proved as above.