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| a part of a line that begins at one point and ends at another |
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| a part of a line that starts at a point and extends infinitely in one direction |
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| a figure formed by two rays with a common endpoint |
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| the point in common of the two rays that form an angle |
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| the region of a plane that falls between the two rays that form an angle (i.e., If two points, one from each side of an angle, are connected by a segment, the segment will pass through the __________ of the angle) |
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| the portion of the plane containing an angle that is not in the angle's interior |
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| to have one or more points in common |
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| the set of all points that two geometric figures have in common |
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| a statement that is accepted as true without proof (__________s are also known as axioms) |
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Having the same size and shape. Segments are __________ if they have the same length. Angles are __________ if they have the same measure.
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| The most common unit of angle measure. When an angle spanning a half circle is divided into 180 equal parts, one of those parts measure one __________. |
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| complementary angles, complement |
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| Two angles whose measures have a sum of 90 degrees. |
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| Two angles whose measures have a sum of 180 degrees. |
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| An angle whose measure is 90 degrees. |
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| An angle whose measure is less than 90 degrees. |
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| An angle whose measure is more than 90 degrees and less than 180 degrees. |
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Two lines that intersect to form a right angle.
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| Two coplanar lines that do not intersect. |
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| A statement that you believe to be true. It is an "educated guess" based on observations. |
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| A line that divides a segment into two congruent segments. |
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| The point where a bisector intersects a segment. |
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| A bisector that is perpendicular to a segment. |
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| A line or ray that divides an angle into two congruent angles. |
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conditional statement
(or conditional) |
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A statement that can be written in the form
"if _____ then _____," where the first blank is the hypothesis and second blank is the conclusion.
Example: "If an animal is an ape, then the animal has opposable thumbs and no tail." |
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The phrase following the word "if" in a conditional statement.
Example: "If an animal is an ape, then the animal has opposable thumbs and no tail." In this conditional "animal is an ape" is the __________. |
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The phrase following the word "then" in a conditional statement.
Example: "If an animal is an ape, then the animal has opposable thumbs and no tail." In this conditional "animal has opposable thumbs and no tail" is the __________.
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| deductive reasoning (deduction) |
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The process of drawing conclusions by using logical reasoning in an argument.
Example
- If a parallelogram has four right angles, then the parallelogram is a rectangle.
- A square is a parallelogram with four right angles.
- Therefore a square is a rectangle.
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converse
(or converse of a conditional) |
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The statement formed by switching the hypothesis and conclusion of a conditional statement to form a new conditional statement.
Example: Given the conditional "If an animal is an ape, then the animal has opposable thumbs and no tail,” the __________ would be "If an animal has opposable thumbs and no tail, then the animal is an ape."
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An example that proves that a statement, often a conjecture, is false.
Example: Given the statement "If an animal is human, then it is a man," a __________ would be ... a woman! |
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A series of logically linked conditional statements. They are linked because the conclusion of one statement is the hypothesis of the next.
Example:
If it is Fall in Oregon, it is raining.
If it is raining, then I stay inside.
If I stay inside, then I get my homework done.
So ... If it is Fall in Oregon, then I get my homework done. |
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A statement using "if and only if."
Example: "A polygon is a triangle if and only if it has three sides." This __________ means the same thing as the following two conditionals:
"If a polygon is a triangle, then it has three sides."
"If a polygon has three sides, then it is a triangle." |
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Euler diagram
(or Venn diagram) |
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A diagram that shows the logical relationships among a number of sets. |
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| A convincing argument that uses logic to show that a statement is true. |
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| Two angles in a plane that share a common vertex and a common side but have no interior points in common. |
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| A statement that has been proven to be true deductively. |
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| The opposite angles formed by two intersecting lines. |
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| inductive reasoning (induction) |
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| Forming conjectures on the basis of observations. |
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| An angle with a measure of 180 degrees. |
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A pair of angles that have one side in common and whose other two sides are rays going in opposite directions to form a line.
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All angles are congruent.
In an equiangular polygon, all of its interior angles have the same measure.
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All sides are congruent.
In an equilateral polygon, all of its sides have the same measure.
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A regular polygon is equiangular and equilateral. That is all of its angles have the same measure, and all of its sides have the same measure.
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a quadrilateral with one pair of parallel sides
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a quadrilateral with two pairs of parallel sides
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a quadrilateral with four congruent sides
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a quadrilateral with four right angles
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a quadrilateral with four congruent sides and four right angles
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a line, ray or segment that intersects two or more coplanar lines, rays or segments, each at a different point
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| The _______________ is a line that divides a planar figure into two congruent, reflected halves, |
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| center (of a regular polygon): |
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| The _______________ is the point that is equidistant from all vertices of a regular polygon. |
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| central angle (of a regular polygon) |
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| The _______________ is an angle whose vertex is the center of a regular polygon and whose sides pass through adjacent vertices. |
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| A _______________ is a polygon in which at least one line segment that connects two vertices of the polygon passes through the polygon’s exterior (a polygon that is not convex). |
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| A _______________ is a polygon in which any line segment that connects two vertices of the polygon passes only through the polygon’s interior |
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| interior angle (of a polygon) |
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| A _______________ is an angle whose vertex is a vertex of a polygon and whose two sides are defined by segments that share that vertex. |
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| exterior angle (of a polygon) |
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| A _______________ is an angle that forms a linear pair with an interior angle. |
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| A _______________ is a closed plane figure formed from three or more segments such that each segment intersects exactly two other segments, one at each endpoint, and no two segments with a common endpoint are collinear. |
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conditional
(or conditional statement) |
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A statement that can be written in the form "if p, then q," where p is the hypothesis and q is the conclusion.
Example: "If an animal is a man, then the animal is a human." In this case "an animal is a man" is the hypothesis, and "the animal is a human" is the conclusion. |
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| The phrase following the word "if" in a conditional statement. |
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| The phrase following the word "then" in a conditional statement. |
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| deductive reasoning (deduction) |
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| The process of drawing conclusions by using logical reasoning in an argument. |
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converse
(or converse of a conditional) |
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| The statement formed by interchanging the hypothesis and conclusion of a conditional statement. |
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An example that proves that a statement, often a conjecture, is false.
Example 1: Given the statement "If an animal is human, then it is a man," a counterexample would be ... a woman!
Example 2: You make a conjecture that every time you add a point to the perimeter of a circle and connect it to every other point by a segment you will double the number of regions. It works for 1, 2, 3, 4 and 5 points: you get 1, 2, 4, 8 and 16 regions. A counterexample is with 6 points. You only get 31 regions. |
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A series of logically linked conditional statements. They are linked because the conclusion of one statement is the hypothesis of the next.
Example:
If it is Fall in Oregon, it is raining.
If it is raining, then I stay inside.
If I stay inside, then I get my homework done.
So ... If it is Fall in Oregon, then I get my homework done. |
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A statement using "if and only if."
Example: "A polygon is a triangle if and only if it has three sides." This biconditional means the same thing as the following two conditionals:
"If a polygon is a triangle, then it has three sides."
"If a polygon has three sides, then it is a triangle." |
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