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24 Cards in this Set
- Front
- Back
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converse |
flip the hypothesis and conclusion; If q, then p. If AB+BC=AC, then B is between A and C. |
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counter-example |
used to prove that an if-then statement is false, For that counter example, the hypothesis is true and the conclusion is false. |
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postulate |
a statement that is accepted without proof |
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theorem |
a statement that can be proved |
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bisector of an angle |
the ray that divides the angle into two congruent adjacent angles |
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bisector of a segment |
a line, segment, ray or plane that intersects the segment at its midpoint |
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Theorem 2-1 midpoint theorem |
if M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB |
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conditional statement |
If p, then q; p implies q; p only if q; q if p |
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biconditional |
if a conditional and its converse are both true they can be combined into a single statement "If and only if" |
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Theorem 2-2 angle bisector |
if ray BX is the bisector of angle ABC, then the measure of angle ABX =1/2 the measure of angle ABC and the measure of angle XBC = 1/2 the measure of angle ABC |
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Theorem 2-3 |
vertical lines are congruent |
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Theorem 2-4 |
If two lines are perpendicular, then they form congruent adjacent angles |
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Theorem 2-5 |
If two lines form congruent adjacent angles, then the lines are perpendicular |
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Theorem 2-6 |
If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary |
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Theorem 2-7 |
If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent |
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Theorem 2-8 |
If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent |
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perpendicular lines |
two lines that intersect to form right angles |
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Definition of perpendicular lines |
If line JK is perpendicular to line MN, then each numbered angle is a right angle |
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Another definition of perpendicular lines |
If only one of the numbered angles is a right angle, then line JK is perpendicular to line MN |
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complementary angles |
two angles whose measures have the sum of 90 |
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supplementary angles |
two angles whose measures have the sum of 180 |
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congruent angles |
angles that have equal measures |
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definition of a midpoint (example) |
line SR is congruent to line RQ |
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definition of a segment bisector (example) |
line PR bisects line SQ |
