Question 1: Calculate the measure of angle x if the alternate interior angles are given as 70° and 70°.

Answer: 70

Question 2: Construct a transversal crossing two lines with angles of 110° and 70°. Are these lines parallel? Explain.

Answer: No, because alternate interior angles are not equal.

Question 3: Determine whether lines l and m are parallel if corresponding angles are 85° and 85°.

Answer: Yes

Question 4: A transversal crosses two lines creating alternate interior angles of 60° and 120°. Are the lines parallel? Show your reasoning.

Answer: No, because alternate interior angles are not equal.

Question 1: Two lines are cut by a transversal. One pair of corresponding angles measures 75°. What is the measure of the other corresponding angles if the lines are parallel? Show your work.

Answer: 75

Question 2: Explain why the following statement is false: 'If two lines have equal angles with a transversal, then they are necessarily parallel.' Provide an example or counterexample.

Answer: Because equal angles alone do not guarantee lines are parallel; they could be intersecting or skew lines.

Question 3: A transversal intersects two lines such that the alternate interior angles are 95° and 85°. Determine if the lines are parallel. Justify your answer.

Answer: No, because alternate interior angles are not equal.

Question 1: A city street has two rows of lamp posts that are perfectly parallel. A pedestrian notices that the lamps on one side are aligned with the lamps directly opposite on the other side, across a crosswalk. Explain how the concept of parallel lines helps in ensuring the street is properly constructed.

Answer: Parallel lines ensure the lamps are aligned and evenly spaced, maintaining symmetry and safety.

Question 2: A carpenter is constructing a bookshelf with two vertical supports that must remain parallel. If the supports are cut at an angle and the angles are measured as 45°, can the supports still be parallel? Explain your reasoning.

Answer: Yes, if the supports are cut at 45°, they can still be parallel; the cut angle does not affect parallelism.

Question 1: Construct a pair of lines and a transversal where the alternate interior angles are 130°. Show that the lines are parallel, and then change one angle to 125° to observe what happens.

Answer: The lines are parallel when angles are 130°, but not when one is 125°.

Question 2: Prove that if two lines are cut by a transversal and one pair of alternate interior angles are equal, then the lines are parallel. Describe all steps involved.

Answer: Since alternate interior angles are equal, by the Converse of Alternate Interior Angles Theorem, the lines are parallel.

Question 1: A student claims: 'If the corresponding angles are 80° and 80°, then the lines are not necessarily parallel.' Is this correct? Explain your reasoning.

Answer: Incorrect. Equal corresponding angles imply the lines are parallel.

Question 2: A diagram shows two lines with a transversal forming alternate interior angles of 60° and 120°, and the student concludes the lines are parallel. Is this correct? Why or why not?

Answer: Incorrect. Because the alternate interior angles are not equal, the lines are not parallel.