Question

1. draw a counterexample that proves the following statement wrong. \if two angles are corresponding angles, then they must both be acute.\

Explanation:

A counter - example is an example that disproves a statement. Corresponding angles are angles in the same relative position with respect to a transversal and two lines. An acute angle is an angle that measures less than \(90^{\circ}\). To disprove the statement, we need to draw a case where two corresponding angles are not acute. When two parallel lines are cut by a transversal, corresponding angles are equal. If the lines are not parallel, we can still have corresponding angles. But for simplicity, consider two parallel lines cut by a transversal. If the transversal is not at a "small" angle. For example, if we have two parallel lines and a transversal such that the corresponding angles are obtuse (an angle greater than \(90^{\circ}\) but less than \(180^{\circ}\)).

Answer:

Draw two parallel lines \(l_1\) and \(l_2\) and a transversal \(t\). Make the angle between the transversal and one of the parallel lines greater than \(90^{\circ}\). The corresponding angles formed (by the transversal with the two parallel lines) will be equal and obtuse (not acute). So this is a counter - example.