Question

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

Explanation:

Step1: Recall the definition of corresponding angles

Corresponding angles are angles that are in the same relative position at each intersection where a straight line crosses two others.

Step2: Recall the definition of acute angles

Acute angles are angles that measure less than \(90^{\circ}\).

Step3: Create a counter - example

Draw two parallel lines cut by a transversal such that the corresponding angles are obtuse (angles greater than \(90^{\circ}\) but less than \(180^{\circ}\)). For example, if we have two parallel lines \(l_1\) and \(l_2\) and a transversal \(t\). Let's assume the measure of one of the corresponding angles is \(120^{\circ}\). Since the lines are parallel, the corresponding angle will also be \(120^{\circ}\) (by the corresponding angles postulate when lines are parallel).

Answer:

Draw two parallel lines cut by a transversal where the corresponding angles are obtuse (e.g., \(120^{\circ}\) each).