Question

1. in the accompanying diagram ( l _ { 1 } parallel l _ { 2 } ) are cut by a transversal ( t ). ( angle 4 ) and ( angle 5 ) can be classified as

(1) vertical angles
(2) same side interior angles
(3) corresponding angles
(4) alternate interior angles

Explanation:

• Vertical angles: These are pairs of opposite angles formed by two intersecting lines. \(∠4\) and \(∠5\) are not opposite each other in this way.
• Same - side interior angles: These are pairs of angles that lie between the two parallel lines (\(l_1\) and \(l_2\)) and on the same side of the transversal \(T\). \(∠4\) and \(∠5\) do not fit this description.
• Corresponding angles: These are pairs of angles in the same relative position. For example, \(∠2\) and \(∠6\) are corresponding angles. \(∠4\) and \(∠5\) are not in the same relative position.
• Alternate interior angles: Alternate interior angles are pairs of angles that lie between the two parallel lines (\(l_1\) and \(l_2\)) and on opposite sides of the transversal \(T\). \(∠4\) and \(∠5\) satisfy this condition.

Answer:

(4) Alternate interior angles