Unit 1, 2, & 3 Definitions, Postulates and Theorems that can be used as Justifications Flashcards
What is the definition of congruent segments?
2 segments with equal lengths
What is the definition of segment betweenness?
If three points are collinear, then the lengths of the smaller segments add up to the length of the entire segment.
What is the definition of midpoint?
A point in the middle of a line segment creating 2 congruent segments.
What is the difference between “Definition of Midpoint” and the “Midpoint Theorem”?
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.
What is the Segment Bisector Theorem?
There is no Segment Bisector Theorem.
What is the definition of segment bisector?
A line ray or segment that goes through the midpoint of a segment, creating two congruent segments.
What is the definition of an acute angle?
An angle with measure less than 90º
What is the definition of an obtuse angle?
An angle with measure greater than 90°
What is the definition of a right angle?
An angle with measure equal to 90°
What is the definition of congruent angles?
2 angles with the same measure (the same number of degrees)
What is the rule involving right angles? (word for word)
All right angles are congruent
What is the definition of adjacent angles?
Two angles that share a common vertex, share a common side, and do not overlap
What is the definition of angle bisector?
A ray that divides an angle in half creating 2 congruent angles
What is the difference between the “Definition of Angle Bisector” and the “Angle Bisector Theorem”?
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.
What is the definition of angle betweenness?
If two angles are adjacent, then the measures of the smaller angles add up to the measure of the entire angle.
What is the rule with vertical angles? (word for word)
Vertical angles are congruent
What is the definition of complementary angles?
2 angles whose measures add up to 90º.
What is the definition of supplementary angles?
2 angles whose measures add up to 180º.
What is the Linear Pair Postulate?
If two angles form a linear pair, then they are supplementary.
What is the definition of linear pair?
Two adjacent supplementary angles.
When is the “definition of linear pair” used as a justification?
Only if it refers to a linear pair of angles as adjacent. Generally, use the linear pair postulate.
What is the definition of perpendicular lines?
2 lines, rays or segments that intersect to form right angles
When do you use the “definition of perpendicular bisector” as a justification?
Never. A justification can be “definition of perpendicular lines” or “ definition of segment bisector” - but we never use the “definition of perpendicular bisector”
What is the definition of parallel lines?
2 coplanar lines that do not intersect
What are the justifications when you have parallel lines?
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.
What are the justifications that prove lines are parallel?
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)
What is the definition of skew lines?
Two noncoplanar lines (that do not intersect)
What are the Properties of Equality that are used to justify algebraic & numeric work with equations?
Addition Property, Subtraction Property, Multiplication Property, Division Property, & Distributive Property.
Explain the reflexive property of equality
The property that justifies any number equals itself.
Explain the symmetric property of equality
The property that justifies switching sides of an equation
Explain the transitive property of equality
The property that justifies “If 2 numbers equal the same 3rd number, then they also equal each other.”
Explain the substitution property of equality
The property that justifies substituting a value for an equal value
Explain the reflexive property of congruence.
The property that justifies any figure is congruent to itself.
Explain the symmetric property of congruence.
The property that justifies switching sides of a congruency.
Explain the transitive property of congruence.
The property that justifies “If 2 figures are congruent to the same 3rd figure, then they are also congruent to each other.”
Explain the substitution property of congruence.
There is no substitution property of congruence.
What is CCAC?
Complements of congruent angles (or the same angle) are congruent.
What is SCAC?
Supplements of congruent angles (or the same angle) are congruent.
