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| may be represented by a dot on a piece of paper, and is usually named by a capital letter. A point has no length, width, or thickness. |
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| an infinite set of points extending endlessly in both directions |
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| A set of points that form a flat surface extending indefinitely in all directions |
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| A set of points consisting of two points on a line, called endpoints, and all of the points on the line between the endpoints |
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| the point of that line segment that divides the segment into two congruent segments. |
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| Bisector of a line segment |
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| any line, or subset of a line, that intersects the segment at its midpoint |
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| The union of two rays having the same endpoint |
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| An angle more than 0 degrees and less than 90 degrees |
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| An angle more than 90 degrees and less than 180 degrees |
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| a ray whose endpoint is the vertex of the angle, and that divides that angle into two congruent angles. |
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| two lines that intersect to form right angles |
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| two lines, both in the same plane, that never intersect |
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| Two angles that share a common ray |
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| Two angles whose sum is 90 degrees |
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| Two angles whose sum is 180 degrees |
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| Two angles that form a straight line |
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| The angles formed opposite each other when two lines intersect |
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| a line that intersects two other coplanar lines in two different points. |
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| Angles that are in the same position on parallel lines. Corresponding angles are congruent. |
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| Alternate Interior Angles |
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| Angles that are on opposite sides of the transversal and on the interior of two parallel lines. Alternate interior angles are congruent. |
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| Same side interior angles |
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| Angles that are on the same side of the transversal and in between two parallel lines. Same side interior angles are supplementary. |
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| A triangle with no sides congruent. |
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| A triangle with two congruent sides and base angles congruent. |
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| A triangle with three congruent sides |
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| A triangle with all three angles less than 90 degrees |
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| A triangle with one right angle |
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| A triangle with one angle greater than 90 degrees |
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| A triangle with all three congruent angles. Each angle measures 60 degrees. |
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| A sentence that can be judged to be true or false |
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| A sentence that contains a variable. |
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| (~) always has the opposite truth value as the original statement |
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formed by combining two simple statements with the word "AND"
A conjunction is only true when they are both true. |
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formed by combining two simple statements using the word "OR"
A disjunction is only false when they are both false |
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| a compound statement formed by using the words IF....THEN to combine two simple sentences. A conditional is only false when it is True arrow False. |
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| The inverse is formed by negating the hypothesis and the conclusion |
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| The converse is formed by switching the order of the hypothesis and the conclusion |
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the contrapositive is formed by by doing the inverse and the converse (switching & negating the hypothesis & conclusion)
The contrapositive is the only one guaranteed to have the same truth value as the original. |
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formed by the phrase if and only if between both simple statements.
the biconditional is only true if they have the same truth values |
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| when a series of particular examples lead to a conclusion |
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| a valid argument that establishes truth using a proof |
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| uses the laws of inference to link together true premises and statments that lead directly to a conclusion |
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| The laws of inference are used to prove that a statement is false leading indirectly to the conclusing that the negation of the statement must be true. |
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| a statement whose truth is accepted without proof |
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| A statement that has been proven |
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A quantity is equal to itself
<A = <A |
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| An equality maybe written in either order |
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| If quantities are qual to the same quantity, they are equal to each other. |
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| A quantity may be substituted for its equal in any expression. |
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| If equal quantities are added to equal quantities, their sums are equal. |
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| If equal quantities are subtracted from equal quantities, their differences are equal. |
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| If equal quantities are multiplied by equal quantities, their products are equal. "Doubles of equals are equal" |
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| If equal quantities are divided by equal quantities, their quotients are equal. "Halves of equals are equal" |
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| Theorem about right angles |
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| All right angles are congruent |
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| Theorem about straight angles |
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| All straight angles are congruent. |
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| Theorems about supplements |
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If two angles are congruent, their supplements are congruent.
If two angles are supplements of the same angle, they are congruent |
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| Theorems about complements |
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Definition
If two angles are congruent, their complements are congruent.
If two angles are complements of the same angle, they are congruent. |
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| a line segment that joins any vertex of a triangle to the midpoint of the opposite side. |
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| a line segment drawn from any vertex of the triangle perpendicular to and ending in the line that contains the opposite side. |
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| a line segment that bisects any angle of the triangle and terminates in the side opposite that angle. |
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| any line or subset of a line that is perpendicular to the line segment at its midpoint. |
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| 5 Ways to Prove that two triangles are congruent |
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| Corresponding Parts of Congruent Triangles are Congruent |
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Where all three perpendicular bisectors meet.
This point is equidistant from all vertices |
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The point where all three medians are concurrent.
This point is the center of gravity.
From vertice to centroid: centroid to midpoint is a 2:1 ratio |
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| The point where all three altitudes meet. |
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The point where all three angle bisectors are concurrent.
The Incenter is equidistant from all sides. |
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| When lines meet at one point. |
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| Three sides of a triangle rule |
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| Any two sides of a triangle must add to be greater than the third |
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| Exterior Angle of a triangle |
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is equal to the sum of the two nonadjacent interior angles.
is greater than either nonadjacent interior angle |
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| Side - Angle Relationship in a triangle |
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| The larger side is across from the larger angle and the smaller side is across from the smaller angle |
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| Given any two quantities, a, b, and c, one and only one of the following is true: a<b, a>b, or a=b. |
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| leg squared + leg squared = hypotenuse squared |
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