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.

Angles e and g are congruent.
https://cdn.fluence.net/image/59c542b617b54a59b4e2c5b3559c1c52 link for image

Answer 1

True statements: 1 and 4.

False statements: 2, 3, and 5.

Let's break down the statements and determine which ones are true based on the information provided in the scenario and the diagram:

Angles B and G are congruent.

True. Corresponding angles formed by the transversal cutting the parallel lines are congruent.

The measures of angles B and C sum to 180 degrees.

False. Angles B and C are not related to each other by any angle relationships. They are on different vertical lines.

Angles C and F are vertical angles.

False. Angles C and F are not opposite each other nor formed by intersecting lines, so they are not vertical angles.

The measures of angles A and H have a sum of 180 degrees.

True. Angles A and H are corresponding angles, and when a transversal crosses parallel lines, corresponding angles are supplementary, meaning their measures sum up to 180 degrees.

Angles E and G are congruent.

False. There's no direct relationship established between angles E and G in the given description.

So, to summarize:

True statements: 1 and 4.

False statements: 2, 3, and 5.