Title: Chapter 2 Free Response
Course: quiz duplicate error

Write the converse of the given true conditional and decide whether the converse is true or false. If the converse is true, combine it with the conditional to form a true biconditional. If the converse is false, give a counterexample.

If two lines are parallel, they do not intersect.

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, state not possible. Explain.

Statement 1: If two lines intersect, then they are not parallel.
Statement 2: [Image] do not intersect.

Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.

If x = 7, then x^2 = 49.

Write the converse of the given true conditional and decide whether the converse is true or false. If the converse is true, combine it with the conditional to form a true biconditional. If the converse is false, give a counterexample.

If the probability that an event will occur is 0, then the event is impossible to occur.

Write the converse of the given true conditional and decide whether the converse is true or false. If the converse is true, combine it with the conditional to form a true biconditional. If the converse is false, give a counterexample.

If two lines are perpendicular, they intersect at right angles.

Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.

If x = 4, then x^2 = 16.

Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.

If x = 8, then x^2 = 64.

For the given statements below, write the first statement as a conditional in if-then form. Then, if possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. Explain.

A right angle has a measure of 90.
[Image] is a right angle.

Write the two conditional statements that form the given biconditional. Then decide whether the biconditional is a good definition. Explain.

Two lines are parallel if and only if they do not intersect.

Give a convincing argument that the following statement is true.

If two angles are congruent and complementary, then the measure of each is 45.

Write the two conditional statements that form the given biconditional.

Three points are collinear if and only if they are coplanar.

For the given statements below, write the first statement as a conditional in if-then form. Then, if possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. Explain.

An acute angle has a measure greater than 0 and less than 90.
[Image] is an acute angle.

Write the two conditional statements that form the given biconditional. Then decide whether the biconditional is a good definition. Explain.

A point is the midpoint of a segment if and only if it is between the endpoints of the segment.

A plumber knows that if you shut off the water at the main valve, it is safe to remove the sink faucet. The plumber turns the main valve to the “Off” position. What conclusion can the plumber make?

Assume that the following statements are true.
i. If Cecil makes his bed, then it is morning.
ii. If it is 8 p.m., then Tami brushes her teeth.
iii. If it is morning, then Ted listens to the radio.
iv. If it is afternoon, then Jeanette takes her daily swim.
v. Cecil makes his bed.
For each statement below, write must be true, may be true, or not true. Use only the information given above. Explain your answers.
a. Ted listens to the radio.
b. Tami does not brush her teeth.
c. Jeanette takes her daily swim.

a. Write the following conditional in if-then form.
b. Write its converse in if-then form.
c. Determine the truth value of the original conditional and its converse. Explain why each of them is true or false, and provide a counterexample(s) for any false statement(s).

On a number line, the points with coordinates –2 and 5 are 7 units apart.

For the given statements below, write the first statement as a conditional in if-then form. Then, if possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. Explain.

A straight angle has a measure of 180.
[Image] is a straight angle.