1.4: Reasoning and Conjectures

What is the sum of the first three consecutive counting numbers starting with 1?

• 6

• 3

• 9

• 12

Which of the following is the correct factorization of the expression 3n + 3?

• n + 1

• 3(n + 1)

• 3n

• n + 3

Which of the following is the Addition Property of Equality?

• If a = b, then a + c = b + c

• If a = b, then a - c = b - c

• If a = b, then ac = bc

• If a = b and c ≠ 0, then a/c = b/c

What should students do to avoid common errors when using properties of equality in algebra?

• Skip steps to save time

• Only use one property for all problems

• Show the property of equality used in each step

• Guess the answer

What is the definition of supplementary angles?

• Angles whose measures add up to 180°

• Angles whose measures add up to 90°

• Angles that are always equal

• Angles that are always adjacent

Which property is demonstrated when a student gives a paper to a second student, who then gives it to a third student, resulting in the same outcome as if the first student had given the paper directly to the third?

• Transitive Property

• Reflexive Property

• Symmetric Property

• Commutative Property

What is a common error students make when solving equations using the Segment or Angle Addition Postulates?

• Forgetting to combine like terms or use inverse operations

• Multiplying instead of adding

• Using the wrong variable

• Ignoring the order of operations

What is the definition of adjacent angles?

• Two angles in the same plane with a common vertex and a common side, but no common interior points.

• Angles that are equal in measure.

• Angles that add up to 180 degrees.

• Angles that are formed by intersecting lines.

According to the postulates about points, lines, and planes, how many lines can be drawn through any two points?

• One

• Two

• Three

• None

Must any two planes intersect? Why or why not?

• No, if the planes are parallel they will never intersect.

• Yes, all planes must intersect.

• Only if the planes are perpendicular.

• Only if the planes are in the same direction.