Question

What is step 3 to complete the proof? a. ap ― ⊥ ra ― by the definition of perpendicular lines b. tr ― ⊥ ra ― by the definition of perpendicular lines c. ra ― | | pt ― by the definition of parallel lines d. tr ― | | ap ― by the definition of parallel lines

Answer 1

The correct step to complete the proof that TRAP is a trapezoid is option A:
`\( TR \parallel AP \)` by the definition of parallel lines.

Detailed Explanation:

In a trapezoid, one pair of opposite sides is parallel. From the given slopes:

- The slope of TR is 3.

- The slope of RA is
`\( -(1)/(2) \)`.

- The slope of AP is 3.

- The slope of PT is
`\( -(3)/(4) \)`.

Since TR and AP have the same slope, they are parallel to each other. The fact that these two sides are parallel is consistent with the definition of a trapezoid, which requires only one pair of opposite sides to be parallel. None of the other sides share the same slope, so they are not parallel to each other, and none form right angles (which would imply perpendicularity). Therefore, TRAP is a trapezoid because it has one pair of parallel sides, which are TR and AP.

Answer 2

To determine the correct step in the proof involving perpendicular and parallel lines, the previous steps or given conditions are necessary. The options provided in the question involve either perpendicular or parallel lines by definition. More context is needed to determine the correct next step.

It seems like you're referring to a geometric proof involving perpendicular and parallel lines. To determine the correct step, I need to know the previous steps or the information provided in the proof. However, based on the options given, it looks like you are trying to establish a relationship between lines. Let me break down the options:

1. a. ap ― ⊥ ra ― by the definition of perpendicular lines
2. b. tr ― ⊥ ra ― by the definition of perpendicular lines
3. c. ra ― || pt ― by the definition of parallel lines
4. d. tr ― || ap ― by the definition of parallel lines

If you have information about the previous steps or any given conditions, I can help you determine which option is the correct next step in the proof. Otherwise, it might be challenging to provide a specific answer without more context.