Question

lesson 24)
complete this sentence with the best of the choices given.

if parallel lines are cut by a transversal, __ angles on the same side of the transversal are __.

Explanation:

To solve this, we recall the properties of parallel lines cut by a transversal. When parallel lines are cut by a transversal, consecutive interior angles on the same side of the transversal are supplementary (their sum is \(180^\circ\)). If we consider the general case of angles on the same side (including corresponding angles, but the key here for same - side interior angles), the correct completion is: If parallel lines are cut by a transversal, \(\boldsymbol{\text{consecutive interior}}\) angles on the same side of the transversal are \(\boldsymbol{\text{supplementary}}\).

(Note: If there were options provided, we would match this with the given options. Since the options are not shown here, we provide the standard geometric answer based on the properties of parallel lines and transversals.)

Answer:

To solve this, we recall the properties of parallel lines cut by a transversal. When parallel lines are cut by a transversal, consecutive interior angles on the same side of the transversal are supplementary (their sum is \(180^\circ\)). If we consider the general case of angles on the same side (including corresponding angles, but the key here for same - side interior angles), the correct completion is: If parallel lines are cut by a transversal, \(\boldsymbol{\text{consecutive interior}}\) angles on the same side of the transversal are \(\boldsymbol{\text{supplementary}}\).

(Note: If there were options provided, we would match this with the given options. Since the options are not shown here, we provide the standard geometric answer based on the properties of parallel lines and transversals.)