Term
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Definition
| If two angles form a linear pair, then the sum of those two angles measurements equals 180 degrees. |
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Term
| Angle Addition Postulates |
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Definition
| A ray is between two other rays with the same vertex if and only if the two divided angles measurements sum up to the whole angle's measurement. |
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Term
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Definition
| Vertical angles are congruent. |
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Term
| SAS, ASA, AAS, SSS, and HL |
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Definition
| All prove triangle congruency. |
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Term
| Isosceles Triangle Theorum |
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Definition
| If triangle(ABC) is a triangle and line segment(AB) is congruent to line segment(AC), then angle(ABC) is congruent to angle(ACB). |
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Term
| Pointwise Characterization of Angle Bisector |
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Definition
| A point(P) lies on the bisector of angle(BAC) if and only if P is on the interior of angle(BAC) and the distance from P to line(AB) equals the distance from P to line(AC). |
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Term
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Definition
| Let triangle(ABC) be a triangle and let line(l) be a line s.t. none of the vertices A,B, and C lie on l. If l intersects line segment(AB), then l also intersects either line segment(BC) or (AC). (Note: But not both!). |
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Term
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Definition
| If D is on the interior of angle(BAC), then there is a point(G) s.t. G lies on both ray(AD) and line segment(BC). |
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Term
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Definition
| If y is a circle, and l is a line s.t. l contains a point that is inside y, then l intersects y consists of exacty two points. |
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Term
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Definition
| Let a and b be two circles. If there exists a point of a that is inside b and there exists another point of a that is outside b, then a intersection b consists of exactly two points. |
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Term
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Definition
| The measure of an exterior angle for a triangle is strictly greater than the measure of either remote interior angle. |
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Term
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Definition
| For every line(l) and for every point(P) that does not lie on l there exists exactly one line(m) s.t. P lies on m and m is parallel with l. |
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Term
| Alternate Interior Angles Theorum |
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Definition
| If l and l' are two lines cut by a transversal t in such a way that a pair of alternate interior angles is congruent, then l is parallel to l'. |
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Term
| Converse to the Alternate Interior Angles Theorum |
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Definition
| If two parallel line are cut by a transversal, then both pairs of alternate interior angles are congruent. |
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Term
| Corresponding Angles Theorum |
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Definition
| If l and l' are lines cut by a transversal t in such a way that two corresponding angles are congruent, then l is parallel to l'. |
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Term
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Definition
| For every triangle, the sum of the measures of the interior angles is 180 degrees. |
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Term
| Pointwise Characterization of Perpendicular Bisector |
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Definition
| A point(P) lies on the perpendicular bisector of line segment(AB) if and only if PA=PB. |
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Definition
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