Question

two mathematicians walk into a bar. the coach says, if two angles are congruent, then they must be corresponding angles. consider each case below. select all the counterexamples to the coachs claim.
o a pair of vertical angles
o a linear - pair of angles
o a pair of angles on the same side of a transversal of parallel lines opening outside the parallel lines
o a pair of angles on opposite sides of a transversal of parallel lines opening inside the parallel lines
o two angles in consecutive corners of a rectangle
o a pair of corresponding angles when a transversal cuts two non - parallel lines

Explanation:

Step1: Define corresponding angles

Corresponding angles are congruent when two parallel lines are cut by a transversal. But other non - corresponding angle pairs can also be congruent.

Step2: Analyze vertical angles

Vertical angles are always congruent. They are not corresponding angles, so they are a counterexample.

Step3: Analyze alternate - interior angles

Alternate - interior angles formed by two parallel lines and a transversal are congruent, but they are not corresponding angles, so they are a counterexample.

Step4: Analyze alternate - exterior angles

Alternate - exterior angles formed by two parallel lines and a transversal are congruent, but they are not corresponding angles, so they are a counterexample.

Answer:

A pair of vertical angles, A pair of alternate - interior angles, A pair of alternate - exterior angles