Question

The Bay City Marina is building a new dock for accessing the slips that boat owners use for docking their boats. The slips can be represented by parallel lines, with the dock cutting across the lines to form slips on either side of the dock. A sketch of the design is show below. Two vertical parallel lines are cut by a transversal from the right to the left shows angles A and B above the transversal and angles E and F below the transversal on the left vertical line and angles C and D above the transversal and angles G and H below the transversal on the right vertical line. The builder needs to know the measures of the angles on the sketch to begin designing support brackets that will connect the new dock to the slips. Which statements are true? Select all that apply. Responses Angles b and g are congruent. Angles b and g are congruent. The measures of angles b and c sum to 180 degrees. The measures of angles b and c sum to 180 degrees. Angles c and f are vertical angles. Angles c and f are vertical angles. The measures of angles a and h have a sum of 180 degrees. The measures of angles a and h have a sum of 180 degrees. Angles e and g are congruent.

Answer 1

The statements that angles b and g are congruent, the measures of angles b and c sum to 180 degrees, and the measures of angles a and h have a sum of 180 degrees are true. The statement that angles c and f are vertical angles is false.

To determine the truth of the statements regarding the angles formed by parallel lines and a transversal, we must apply our knowledge of geometry, specifically the properties of angles created when parallel lines are intersected by a transversal. Angles that are on the opposite sides of the transversal and inside the parallel lines are called alternate interior angles, and they are congruent.

Angles b and g are congruent: This is true, as they are alternate interior angles.

The measures of angles b and c sum to 180 degrees: This is true, as they are consecutive interior angles on the same side of the transversal.

Angles c and f are vertical angles: This is false, they are not formed by the same intersection and therefore are not vertical angles.

The measures of angles a and h have a sum of 180 degrees: This is true, as they are also consecutive interior angles on the same side of a transversal.

Angles e and g are congruent: This is true, because they are alternate interior angles as well.