To determine which statement could be proved using a diagram, we can analyze each option:
a. Alternate interior angles are congruent - This can be easily illustrated with a diagram showing a pair of parallel lines cut by a transversal, where the alternate interior angles would be shown as congruent.
b. The Pythagorean Theorem - While a diagram can help visualize the relationship among the sides of a right triangle, proving the theorem typically requires more than a mere diagram.
c. Two lines are parallel if they have the same slope - This can also be visually supported by a diagram of two lines on a coordinate plane showing that lines with the same slope do not intersect and therefore are parallel.
d. The Triangle Sum Theorem - This theorem states that the sum of the interior angles of a triangle is 180 degrees. This can be illustrated with a diagram of a triangle clearly showing how the angles add up to 180 degrees.
Among these, option a (Alternate interior angles are congruent) is often the most straightforward and commonly proved using a diagram of parallel lines and a transversal. Thus, while all options can be illustrated or supported by diagrams, option a is particularly suitable for proof with a diagram.
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