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Parallel lines |
Two lines that lie in the same plane and do not intersect. |
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Perpendicular lines |
Two lines that intersect to form a right angle. |
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Skew lines |
Two lines that do not lie in the same plane and do not intersect |
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Parallel planes |
Two planes that do not intersect |
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Transversal |
A line that intersects two or more coplanar lines at different points |
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Corresponding angles |
Two angles formed by two lines and a transversal, and occupy corresponding positions |
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Alternate interior angles |
Two angles formed by two lines and a transversal and lie between the two lines on the opposite sides of the transversal |
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Alternate exterior angles |
Two angles formed by two lines and a transversal and lie outside the two lines on the opposite sides of the transversal |
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Same-side interior angles |
Two angles formed by two lines and a transversal and lie between the two lines on the same side of the transversal |
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Converse |
The statement formed by switching the hypothesis and the conclusion in an if-then statement |
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Hypothesis |
The "if" part of an if-then statement |
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Conclusion |
The "then" part of an if-then statement |
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All right angles are ____________ |
congruent |
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If two lines are perpendicular, then they intersect to form four _______ ________. |
right angles |
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If two lines intersect to form adjacent congruent angles, then the lines are _____________________. |
perpendicular |
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If two sides of adjacent acute angles are perpendicular, then the angles are ___________________. |
complementary |
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If two parallel lines are cut by a transversal, then ______________ interior angles are congruent. |
alternate |
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If two parallel lines are cut by a transversal, then _____________ exterior angles are congruent. |
alternate |
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If two parallel lines are cut by a transversal, then _______________ interior angles are supplementary. |
same-side |
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If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are ___________________. |
parallel |
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If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are _____________________. |
parallel |
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If two lines are cut by a transversal so that same-side interior angles are _________________, then the lines are parallel. |
supplementary |
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If two lines are parallel to the same line, then they are _________ to each other. |
parallel |
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In a plane, if two lines are perpendicular to the same line, then they are ___________ to each other. |
parallel |
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Midpoint |
The point on a segment that divides the segment into two equal parts. |
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Segment bisector |
Something that intersects a segment at it’s midpoint. |
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Bisect |
To divide into two congruent parts. |
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Angle bisector |
A ray that divides an angle into two equal angles. |
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Complementary angles |
Two angles whose measures have a sum of 90 degrees. |
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Supplementary angles |
Two angles whose measure has a sum of 180 degrees. |
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Adjacent angles |
Two angles with a common vertex and side but no common interior points. |
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Theorem |
A true statement that follows from other true statements. |
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Vertical angles |
Two nonadjacent angles formed by two intersecting lines. |
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Linear pair |
Two adjacent angles whose noncommon sides are on the same line (supplementary). |
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If-then statements |
A statement with a hypothesis (if) and conclusion (then). |
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Deductive reasoning |
Using facts, definitions, accepted properties to make a logical argument. |
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Congruent complements theorem |
If two angles are complementary to the same angle, then they are congruent. |
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Congruent supplements theorem |
If two angles are supplements to the same angle, then they are congruent. |
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Vertical angles theorem |
Vertical angles are congruent. |
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Reflexive Property |
A=A |
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Symmetric Property |
If A=B, then B=A |
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Transitive Property |
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2.1 Congruent Complements Theorem |
If two angles are complements to the same angle, then they are congruent. |
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2.2 Congruent Supplements Theorem |
If two angles are supplements to the same angle, then they are congruent. |
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2.3 Vertical Angles Theorem |
When two lines intersect, they form two sets of vertical angels. Vertical angles are congruent. <a=<b |
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angle |
a geometric figure formed by two rays with a common end point |
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protractor |
a tool used to measure angles |
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acute angle |
an angle that is greater than 0 degrees and less than 90 degrees |
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right angle |
an angle that equals 90 degrees |
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obtuse angle |
an angle that is greater than 90 degrees and less than 180 degrees |
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straight angle |
an angle equal to 180 |
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adjacent angle |
two angles that have a common vertex and a common ray |
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complementary angles |
a pair of angles whose measures have the sum of 90 degrees |
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supplementary angles |
a pair of angles whose measures have the sum of 180 degrees |
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congruent angles |
angles that have the same measure |
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vertical angles |
angles formed by intersecting lines |
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angle bisector |
a ray that divides an angle into two congruent angles |
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inductive reasoning |
reasoning that a statement or rule is true because specific cases are true |
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law of detachment |
says 1. if p then q 2. p so we can get a third statement 3. q |
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law of syllogism |
says 1. if p then q 2. if q then r so we get a third statement 3. if p then r |
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