Unit 02 Practice

The midpoint of segment AC is located at (0, 1), and one endpoint of this segment has coordinates of (-3, 6). What are the other coordinates of the other endpoint of segment AC?

• (3, -4)

• (-1.5, 3.5)

• (2, -6)

• (0, -3)

Point D is located halfway between points A and B. What is the shortest distance from C to D, rounded to the nearest tenth?

• 14.4

• 5.4

• 12.8

• 16.9

Billy made the following conjecture: If two parallel lines are cut by a transversal, then the alternate exterior angles are supplementary.

Based on the information in the figures given, which of the following is a reasonable conclusion?

• Alternate exterior angles are not supplementary in figure 1. The conjecture is false because this provides a counterexample.

• Alternate exterior angles are supplementary in figure 2. This is proof that makes this conjecture a theorem.

• Alternate exterior angles are not supplementary in figure 1, but are supplementary in figure 2. Since these don't match, we cannot say whether the conjecture is true or false.

A true conditional statement is given below:

"If a closed-sided figure has three sides, then it is a triangle."

Identify the inverse statement of the conditional statement and determine if the inverse is true or false.

• "If a closed-sided figure does not have three sides, then it is not a triangle."

  True

• "If a closed-sided figure is not a triangle, then it does not have three sides."

  True

• "If a closed-sided figure is a triangle, then it has three sides."

  True

• "If a closed-sided figure does not have three sides, then it is not a triangle."

  False

Taylor made the following conjecture: "For all real numbers x, 3x is greater than or equal to x."

Which of the following values of x can be used as a counterexample to disprove Taylor's conjecture?

• x = 2

• x = 1

• x = 1.5

• x = -1

The shortest distance between two points along the surface of the earth is....

• a straight line

• an arc

• a circle

• a ray

Line a is parallel to line b, and line a and line b are cut by three transversals. Based on the angles formed by the transversals, which two conjectures about the relationships of the angles are true?

• Alternate exterior angles are congruent.

• Corresponding angles are congruent.

• Same side interior angles are congruent.

• Alternate interior angles are supplementary.

Which conjecture explains the relationship between the angles in the construction below?

• Angle CAF is congruent to angle BAF.

• Angle CAF is congruent to angle CAB.

• Angle CAF is half of angle BAF.

• Angle CAF is two times angle CAB.

The measure of ∠P is 156° and the measure of ∠M is one third of the measure of ∠P. What is the measure of ∠N?

• 52°

• 128°

• 24°

• 136°

Find the length of the hypotenuse.

• 35

• 19

• 40

• 38