Term
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Definition
A(n) __________ is 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 a vehicle is a long board, then the vehicle has four wheels. |
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Term
| hypothesis (of a conditional statement) |
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Definition
| The __________ is the clause following the words “if” in a conditional statement |
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Term
| conclusion (of a conditional statement) |
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Definition
| The __________ is the clause following the word “then” in a conditional statement |
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Term
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Definition
| A(n) __________ is a diagram composed of closed shapes used to illustrate the logical relationship among sets of objects. It is useful for illustrating conditional statements. |
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Term
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Definition
| A(n) __________ is an object that proves a conditional statement false. The object must fit the hypothesis but not the conclusion. |
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Term
| converse (of a conditional statement) |
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Definition
| The __________ is a conditional statement formed by switching the hypothesis and conclusion of a conditional statement. An original statement “If p then q” becomes “If q then p” |
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Term
| biconditional (statement) |
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Definition
A(n) __________ is a conditional statement that is true both “forward” and “backward” and is written using “Iff” or “If and only if”
Example:
"A quadrilateral is a rectangle if and only if it has four right interior angles" or "Iff a quadrilateral is a rectangle, then it has four right interior angles." |
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Term
| inverse (of a conditional statement) |
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Definition
| The __________ is a conditional statement formed by negating both the hypothesis and conclusion of a conditional statement. An original statement “If p then q” becomes “If not p then not q.” |
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Term
| contrapositive (of a conditional statement) |
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Definition
| The __________ is a conditional statement formed by first negating both the hypothesis and conclusion of a conditional statement and then switching them. An original statement “If p then q” becomes “If not q then not p.” This form of a true conditional statement is always true. |
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Term
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Definition
| __________ is the process of drawing logically certain conclusions using an argument. |
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Term
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Definition
| If two geometric figures are __________, then they lie on the same line. |
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Term
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Definition
| If two geometric figures are __________, then they lie on the same plane. |
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Term
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Definition
| If a figure is a(n) __________, then it is part of a line that begins at one point on a line and ends at another point on the line. |
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Term
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Definition
| If a figure is a(n) __________, then it is a part of a line that starts at a point on the line and extends infinitely in one direction. |
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Term
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Definition
| If a figure is a(n) __________, then it is formed by two rays with a common endpoint. |
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Term
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Definition
| If a point is the __________ of an angle, then it lies on both rays that form the angle. |
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Term
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Definition
| The __________ is the region of a plane that falls between the two rays that form an angle. |
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Term
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Definition
| The __________ is the portion of the plane containing an angle that is not in the angle's interior. |
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Term
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Definition
| A(n) __________ is a statement that is accepted as true without proof. |
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Term
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Definition
| A(n) __________ is a statement that you believe to be true. It is an “educated guess” based on observations |
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Term
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Definition
| A(n) __________ is a convincing argument that uses logic to show that a statement must be true |
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Term
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Definition
| A(n) __________ is a statement that has been proven true using deductive reasoning |
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Term
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Definition
| If the two rays that form the sides of an angle form a straight line, then we call the angle a(n) __________. If an angle is a(n) __________, then we say it has a measure of 180°. |
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Term
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Definition
| If two angles share a vertex and some interior points, then we call the angles __________. |
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Term
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Definition
| If two angles share a vertex and a side, but have no interior points in common, then we call the pair of angles __________. |
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Term
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Definition
| If the non-shared sides of a pair of adjacent angles form a straight line, then we call the pair of angles a(n) __________. |
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Term
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Definition
| If two angles formed by two lines that cross are non-adjacent and non-overlapping, then they are called __________. |
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Term
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Definition
| If a line crosses two or more other lines, each at a different point, then we call the first line a(n) __________. |
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Term
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Definition
| If two non-adjacent angles formed by a transversal and two of the lines it crosses are on the same side of the transversal, but one is on the interior of the two lines the transversal crosses and one is in the exterior, then we call the angles __________. |
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Term
| alternate interior angles |
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Definition
| If two of the angles formed by a transversal and two of the lines it crosses are on opposite sides of the transversal and in the interior of the two lines crossed, then we call them __________. |
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Term
| alternate exterior angles |
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Definition
| If two of the angles formed by a transversal and two of the lines it crosses are on opposite sides of the transversal and in the exterior of the two lines crossed, then we call them __________. |
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Term
| same-side interior angles |
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Definition
| If two of the angles formed by a transversal and two of the lines it crosses are on the same side of the transversal and in the interior of the two lines crossed, then we call them __________. |
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Term
| same-side exterior angles |
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Definition
| If two of the angles formed by a transversal and two of the lines it crosses are on the same side of the transversal and in the exterior of the two lines crossed, then we call them __________. |
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Term
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Definition
| Iff a plane figure is 1) closed 2) formed from three or more segments such that each segment intersects exactly two other segments, one at each endpoint, and 3) no two segments with a common endpoint are collinear, then the plane figure is a(n) __________. |
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Term
| vertex (of a polygon), vertices |
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Definition
| Iff a point is the intersection of two sides of a polygon, then the point is a(n) __________ of the polygon. |
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Term
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Definition
| Iff a segment connects two non-adjacent vertices of a polygon, then the segment is a(n) __________ of that polygon. |
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Term
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Definition
| Iff every diagonal of a polygon passes only through the polygon’s interior, then the polygon is a convex polygon. |
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Term
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Definition
| Iff at least one diagonal of a polygon passes through the polygon’s exterior then the polygon is a(n) __________ polygon. |
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Term
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Definition
| Iff all the interior angles of a polygon have the same measure, then the polygon is a(n) __________ polygon. |
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Term
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Definition
| Iff all the segments that form a polygon have the same measure, then the polygon is a(n) __________ polygon. |
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Term
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Definition
| Iff a polygon is both equiangular and equilateral, then the polygon is a(n) __________ polygon. |
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Term
| center (of a regular polygon) |
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Definition
| Iff a point is equidistant from all vertices of a regular polygon, then the point is the __________ of the regular polygon. |
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Term
| central angle (of a regular polygon) |
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Definition
| Iff an angle’s vertex is the center of a regular polygon, and the angle’s sides pass through adjacent vertices of the polygon, then the angle is a(n) __________ of that regular polygon. |
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Term
| interior angle (of a polygon) |
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Definition
| Iff an angle’s vertex is a vertex of a polygon, and if the angle’s sides are segments that share that vertex, then the angle is a(n) __________ of the polygon. |
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Term
| exterior angle (of a convex polygon) |
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Definition
| Iff an angle forms a linear pair with an interior angle of a convex polygon, then it is a(n) __________ of the convex polygon. |
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Term
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Definition
| Iff a polygon has four sides, then the polygon is a(n) __________. |
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Term
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Definition
| Iff a polygon has five sides, then the polygon is a(n) __________. |
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Term
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Definition
| Iff a polygon has six sides, then the polygon is a(n) __________. |
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Term
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Definition
| Iff a polygon has seven sides, then the polygon is a(n) __________. |
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Term
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Definition
| Iff a polygon has eight sides, then the polygon is a(n) __________. |
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Term
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Definition
| Iff a polygon has n sides, then the polygon is an n-gon. |
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