Question

Statement 1: If parallel lines have a transversal, then corresponding angles are congruent. Statement 2: A line has an infinite number of points extending in opposite directions. Which geometry term does each statement represent?

Answer 1

Statement 1 represents the principle of corresponding angles, stating that if parallel lines are crossed by a transversal, the corresponding angles are congruent. Statement 2 describes the definition of a line, which is infinite in length and has an infinite number of points.

Step-by-step explanation:

The geometry terms represented by the statements provided include corresponding angles and line.

Statement 1: If parallel lines have a transversal, then corresponding angles are congruent. This statement represents the principle of corresponding angles. In geometry, when two parallel lines are crossed by a transversal, the angles in matching corners are called corresponding angles, and they are congruent, meaning they have the same measure.

Statement 2: A line has an infinite number of points extending in opposite directions. This statement describes the basic definition of a line in geometry. A line is indeed infinite in length, extending forever in both directions, and contains an infinite number of points along its length.

Answer 2

The statement 1:"If parallel lines have a transversal, then corresponding angles are congruent" is theorem, because it has been proved. It is a logical consequence of axioms.
The statement 2:"A line has an infinite number of points extending in opposite directions." is postulate or also referred as axiom, because is taken to be true without proof. Is it a true statement that can not be proven.