When performing a construction, what are the only tools needed to complete the construction?(1 point)

Question

Responses

only a ruler
only a ruler

only a compass
only a compass

a compass and a straightedge
a compass and a straightedge

a compass, a straightedge, and a ruler

Answer 1

The correct response is:

a compass and a straightedge

These two tools are sufficient for performing classical constructions in geometry, allowing you to create circles and straight lines, which can be used to construct various geometric shapes and figures.

Answer 2

Select the choice that indicates AB←→ is the perpendicular bisector of CD←→ if they intersect at P .(1 point)
Responses

AP¯¯¯¯¯¯¯¯≅BP¯¯¯¯¯¯¯¯
Modifying above upper A upper P with bar congruent to Modifying above upper B upper P with bar

AC¯¯¯¯¯¯¯¯⊥BD¯¯¯¯¯¯¯¯ and AP¯¯¯¯¯¯¯¯≅BP¯¯¯¯¯¯¯¯
Modifying above upper A upper C with bar perpendicular to Modifying above upper B upper D with bar and Modifying above upper A upper P with bar congruent to Modifying above upper B upper P with bar

AB¯¯¯¯¯¯¯¯⊥CD¯¯¯¯¯¯¯¯ and CP¯¯¯¯¯¯¯¯≅DP¯¯¯¯¯¯¯¯
Modifying above upper A upper B with bar perpendicular to Modifying above upper C upper D with bar and Modifying above upper C upper P with bar congruent to Modifying above upper D upper P with bar

CD¯¯¯¯¯¯¯¯⊥AB¯¯¯¯¯¯¯¯

Answer 3

The choice that indicates \( AB \longleftrightarrow \) is the perpendicular bisector of \( CD \longleftrightarrow \) if they intersect at \( P \) is:

AC¯¯¯¯¯¯¯¯⊥BD¯¯¯¯¯¯¯¯ and AP¯¯¯¯¯¯¯¯≅BP¯¯¯¯¯¯¯¯

This statement indicates that line segment \( AC \) is perpendicular to \( BD \) and that segments \( AP \) and \( BP \) are congruent, which are the required conditions for \( AB \) to be the perpendicular bisector of \( CD \).

Answer 4

Identify one of the steps necessary to construct a parallel line to a given line through a point not on the line.(1 point)
Responses

With the pointed tip of your compass on a point on the given line, draw an arc that extends both above and below the given line.
With the pointed tip of your compass on a point on the given line, draw an arc that extends both above and below the given line.

After drawing a given line and a point not on the line, fold your paper so that the fold goes through the point not on the line.
After drawing a given line and a point not on the line, fold your paper so that the fold goes through the point not on the line.

With the pointed tip of your compass on a point on the given line, draw an arc that intersects the given line and the line drawn from the point on the given line to the point not on the given line.
With the pointed tip of your compass on a point on the given line, draw an arc that intersects the given line and the line drawn from the point on the given line to the point not on the given line.

Place the edge of a ruler on the given line and slide the ruler up or down until it is aligned with the point, then draw a line through the point.

Answer 5

The correct response for one of the steps necessary to construct a parallel line to a given line through a point not on the line is:

With the pointed tip of your compass on a point on the given line, draw an arc that extends both above and below the given line.

This step is part of the process of creating congruent angles to ensure that the new line drawn will be parallel to the given line.

Answer 6

Which statement is true for all parallel lines?(1 point)
Responses

Parallel lines have a slope of zero.
Parallel lines have a slope of zero.

Parallel lines have the same slope.
Parallel lines have the same slope.

Parallel lines have slopes that are undefined.
Parallel lines have slopes that are undefined.

Parallel lines have slopes that are negative reciprocals of each other.

Answer 7

The correct response is:

Parallel lines have the same slope.

This statement is true for all parallel lines, regardless of whether they are horizontal, vertical, or slanted. The slopes of parallel lines are equal.