HW 1-8

When two parallel lines are cut by a transversal and two angles are picked at random, there are only two possible numerical outcomes. What are the two outcomes? Choose ALL that apply.

• The angles are complementary.

• The angles are supplementary.

• The measures of the angles are equal.

• The angles are adjacent.

m∠2 = 37°. What is m∠8? (In the diagram, the lines that appear to be parallel are parallel. Diagram is not drawn to scale.)

• 37°

• 53°

• 74°

• 143°

Jason is given the m∠5 = 148°. What theorem allows Jason to conclude that m∠4 = 148°? (In the diagram, the lines that appear to be parallel are parallel. Diagram is not drawn to scale.)

• Vertical Angles Theorem

• Corresponding Angles Theorem

• Alternate Interior Angles Theorem

• Same Side Interior Angles Theorem

m∠1 = 129° and m∠6 is 12x + 3. Based on this information, which statement below is a true statement? (In the diagram, the lines that appear to be parallel are parallel. Diagram is not drawn to scale.)

• (12x + 3) + 129 = 180

• (12x + 3) + 129 = 90

• (12x + 3) + 129 = 360

• 12x – 3 = 129

m∠1 = 129° and m∠6 is 12x + 3. What is the value of x? (In the diagram, the lines that appear to be parallel are parallel. Diagram is not drawn to scale.)

• 10.5

• 19

• 4

• 18.5

Jimmy picks two angles from the diagram at random. The angles share a vertex and are across from each other. Which theorem can Jimmy use to prove that the two angles are congruent? (In the diagram, the lines that appear to be parallel are parallel. Diagram is not drawn to scale.)

• Vertical Angles Theorem

• Linear Pair Theorem

• Same Side Interior Angles Theorem

• Definition of Supplementary Angles

Paula states that ∠A and ∠B form a linear pair. She then concludes that m∠A + m∠B = 180° because of the Linear Pair Theorem. Describe Paula’s error.

• Paula should use the Linear Pair Theorem to conclude that m∠A = m∠B.

• Paula was using the Definition of a Linear Pair, not the Linear Pair Theorem.

• Paula should have concluded that ∠A and ∠B are supplementary and then use the Definition of Supplementary to conclude that m∠A + m∠B = 180°.

• Paula did not make an error. Paula’s conclusion is the correct conclusion.

The Vertical Angles Theorem states that if two angles are vertical angles, then they are congruent. Tony has two congruent angles. Based on this information, which statement is a true statement?

• The two angles are vertical angles.

• The measures of the two angles are equal.

• The two angles are adjacent angles.

• The two angles are supplementary.

Mary constructs parallel lines (as shown at right). What basic construction is used to construct parallel lines?

• Copy a segment.

• Perpendicular Bisector

• Copy an angle

• Angle Bisector

Andrea constructs perpendicular lines (as shown at right). What basic construction is used to construct perpendicular lines?

• Copy a segment.

• Perpendicular Bisector

• Copy an angle

• Angle Bisector