Unit 1, 2, & 3 Definitions, Postulates and Theorems that can be used as Justifications

Question 1

What is the definition of congruent segments?

Answer 1

2 segments with equal lengths

Question 2

What is the definition of segment betweenness?

Answer 2

If three points are collinear, then the lengths of the smaller segments add up to the length of the entire segment.

Question 3

What is the definition of midpoint?

Answer 3

A point in the middle of a line segment creating 2 congruent segments.

Question 4

What is the difference between “Definition of Midpoint” and the “Midpoint Theorem”?

Answer 4

The “Definition of Midpoint” compares the 2 smaller segments. The “Midpoint Theorem” compares the length of the smaller segment to the length of the larger segment.

Question 5

What is the Segment Bisector Theorem?

Answer 5

There is no Segment Bisector Theorem.

Question 6

What is the definition of segment bisector?

Answer 6

A line ray or segment that goes through the midpoint of a segment, creating two congruent segments.

Question 7

What is the definition of an acute angle?

Answer 7

An angle with measure less than 90º

Question 8

What is the definition of an obtuse angle?

Answer 8

An angle with measure greater than 90°

Question 9

What is the definition of a right angle?

Answer 9

An angle with measure equal to 90°

Question 10

What is the definition of congruent angles?

Answer 10

2 angles with the same measure (the same number of degrees)

Question 11

What is the rule involving right angles? (word for word)

Answer 11

All right angles are congruent

Question 12

What is the definition of adjacent angles?

Answer 12

Two angles that share a common vertex, share a common side, and do not overlap

Question 13

What is the definition of angle bisector?

Answer 13

A ray that divides an angle in half creating 2 congruent angles

Question 14

What is the difference between the “Definition of Angle Bisector” and the “Angle Bisector Theorem”?

Answer 14

The “Definition of Angle Bisector” compares the smaller angle to the other smaller angle. The “Angle Bisector Theorem” compares the measure of the smaller angle to the measure of the larger angle.

Question 15

What is the definition of angle betweenness?

Answer 15

If two angles are adjacent, then the measures of the smaller angles add up to the measure of the entire angle.

Question 16

What is the rule with vertical angles? (word for word)

Answer 16

Vertical angles are congruent

Question 17

What is the definition of complementary angles?

Answer 17

2 angles whose measures add up to 90º.

Question 18

What is the definition of supplementary angles?

Answer 18

2 angles whose measures add up to 180º.

Question 19

What is the Linear Pair Postulate?

Answer 19

If two angles form a linear pair, then they are supplementary.

Question 20

What is the definition of linear pair?

Answer 20

Two adjacent supplementary angles.

Question 21

When is the “definition of linear pair” used as a justification?

Answer 21

Only if it refers to a linear pair of angles as adjacent. Generally, use the linear pair postulate.

Question 22

What is the definition of perpendicular lines?

Answer 22

2 lines, rays or segments that intersect to form right angles

Question 23

When do you use the “definition of perpendicular bisector” as a justification?

Answer 23

Never. A justification can be “definition of perpendicular lines” or “ definition of segment bisector” - but we never use the “definition of perpendicular bisector”

Question 24

What is the definition of parallel lines?

Answer 24

2 coplanar lines that do not intersect

Question 25

What are the justifications when you have parallel lines?

Answer 25

If 2 lines are parallel, then the corresponding angles are congruent. If 2 lines are parallel, then the alternate interior angles are congruent. If 2 lines are parallel, then the same side interior angles are supplementary. If 2 lines are parallel, then the alternate exterior angles are congruent. If 2 lines are parallel, then the same side exterior angles are supplementary. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Question 26

What are the justifications that prove lines are parallel?

Answer 26

If corresponding angles are congruent, then the lines are parallel. If alternate interior angles are congruent, then the lines are parallel. If alternate exterior angles are congruent, then the lines are parallel. If same side interior angles are supplementary, then the lines are parallel. If same side exterior angles are supplementary, then the lines are parallel. If two coplanar lines are perpendicular to the same line, then they are parallel. If two lines are parallel to a third line, then they are parallel to each other. (The transitive property of parallel lines)

Question 27

What is the definition of skew lines?

Answer 27

Two noncoplanar lines (that do not intersect)

Question 28

What are the Properties of Equality that are used to justify algebraic & numeric work with equations?

Answer 28

Addition Property, Subtraction Property, Multiplication Property, Division Property, & Distributive Property.

Question 29

Explain the reflexive property of equality

Answer 29

The property that justifies any number equals itself.

Question 30

Explain the symmetric property of equality

Answer 30

The property that justifies switching sides of an equation

Question 31

Explain the transitive property of equality

Answer 31

The property that justifies "If 2 numbers equal the same 3rd number, then they also equal each other."

Question 32

Explain the substitution property of equality

Answer 32

The property that justifies substituting a value for an equal value

Question 33

Explain the reflexive property of congruence.

Answer 33

The property that justifies any figure is congruent to itself.

Question 34

Explain the symmetric property of congruence.

Answer 34

The property that justifies switching sides of a congruency.

Question 35

Explain the transitive property of congruence.

Answer 35

The property that justifies "If 2 figures are congruent to the same 3rd figure, then they are also congruent to each other."

Question 36

Explain the substitution property of congruence.

Answer 36

There is no substitution property of congruence.

Question 37

What is CCAC?

Answer 37

Complements of congruent angles (or the same angle) are congruent.

Question 38

What is SCAC?

Answer 38

Supplements of congruent angles (or the same angle) are congruent.