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111 Cards in this Set
- Front
- Back
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Reflexive property |
a = a
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a = a
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Reflexive property
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If a = b, then can be substituted for in any expression.
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Substitution property
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Substitution property
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If a = b, then a can be substituted for b in any expression.
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Addition property of equality
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If a = b then a + c = b + c (Whatever you add to one side you must add to the other.)
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If a = b then a + c = b + c (Whatever you add to one side you must add to the other.)
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Addition property of equality
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If a = b then a - c = b - c (Whatever you subtract from one side you must subtract from the other.)
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Subtraction property of equality. |
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Subtraction property of equality.
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If a = b then a - c = b - c (Whatever you subtract from one side you must subtract from the other.) |
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Multiplication property of equality.
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If a = b then a • c = b • c (Whatever you multiply to one side you must multiply to the other.)
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If a = b then a • c = b • c (Whatever you multiply to one side you must multiply to the other.)
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Multiplication property of equality. |
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If a = b then a ÷ c = b ÷ c (Whatever you divide on one side you must divide on the other.)
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The division property of equality.
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The division property of equality.
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If a = b then a ÷ c = b ÷ c (Whatever you divide on one side you must divide on the other.) |
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(number line) coordinate
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Every point on a line corresponds to exactly one real number called its...
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Every point on a line corresponds to exactly one real number called its...
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(number line) coordinate
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To every pair of points on a line there corresponds a real number called the...
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distance
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distance
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To every pair of points on a line there corresponds a real number called the...
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The Ruler Postulate
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The points on a line can be numbered so that positive number differences measure distances. |
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The points on a line can be numbered so that positive number differences measure distances.
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The Ruler Postulate
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A - B - C
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states betweenness, and is read “B is between A and C”.
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states betweenness, and is read “B is between A and C”.
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A - B - C
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Betweenness of points
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A point is between two other points on the same line iff its coordinate is between their coordinates. |
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A point is between two other points on the same line iff its coordinate is between their coordinates. |
Betweenness of points
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The Betweenness of Points Theorem
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If A - B - C, then AB + BC = AC
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If A - B - C, then AB + BC = AC
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The Betweenness of Points Theorem
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degree
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A unit for measuring angles.
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A unit for measuring angles.
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degree
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Number of degrees in a circle.
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360
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360
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Number of degrees in a circle.
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A half-rotation of rays...
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is all of the rays that correspond to a common protractor. (The rays in a half-circle.) |
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The rays that correspond to a common protractor is... |
a half-rotation of rays... |
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(protractor) coordinate
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The rays in a half-rotation can be numbered so that to every ray there corresponds exactly one real number called its... |
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The rays in a half-rotation can b numbered so that to every ray there corresponds exactly one real number called its... |
coordinate |
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The Protractor Postulate |
The rays in a half-rotation can be numbered from 0 to 180 so that positive number differences measure angles.
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The rays in a half-rotation can be numbered from 0 to 180 so that positive number differences measure angles. |
The Protractor Postulate
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If an angle is acute... |
then it is less than 90°. |
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Reflexive property
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a = a
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a = a
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Reflexive property
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If a = b, then can be substituted for in any expression.
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Substitution property
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Substitution property
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If a = b, then a can be substituted for b in any expression.
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Addition property of equality
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If a = b then a + c = b + c (Whatever you add to one side you must add to the other.)
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If a = b then a + c = b + c (Whatever you add to one side you must add to the other.)
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Addition property of equality
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If a = b then a - c = b - c (Whatever you subtract from one side you must subtract from the other.)
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Subtraction property of equality. |
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Subtraction property of equality.
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If a = b then a - c = b - c (Whatever you subtract from one side you must subtract from the other.) |
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Multiplication property of equality.
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If a = b then a • c = b • c (Whatever you multiply to one side you must multiply to the other.)
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If a = b then a • c = b • c (Whatever you multiply to one side you must multiply to the other.)
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Multiplication property of equality. |
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If a = b then a ÷ c = b ÷ c (Whatever you divide on one side you must divide on the other.) |
The division property of equality. |
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The division property of equality.
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If a = b then a ÷ c = b ÷ c (Whatever you divide on one side you must divide on the other.)
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(number line) coordinate
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Every point on a line corresponds to exactly one real number called its...
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Every point on a line corresponds to exactly one real number called its...
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(number line) coordinate
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To every pair of points on a line there corresponds a real number called the...
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distance
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distance
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To every pair of points on a line there corresponds a real number called the...
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The Ruler Postulate
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The points on a line can be numbered so that positive number differences measure distances.
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The points on a line can be numbered so that positive number differences measure distances.
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The Ruler Postulate
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A - B - C
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states betweenness, and is read “B is between A and C”.
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states betweenness, and is read “B is between A and C”.
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A - B - C
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Betweenness of points
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A point is between two other points on the same line iff its coordinate is between their coordinates.
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A point is between two other points on the same line iff its coordinate is between their coordinates.
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Betweenness of points
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The Betweenness of Points Theorem
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If A - B - C, then AB + BC = AC
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If A - B - C, then AB + BC = AC
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The Betweenness of Points Theorem
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degree
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A unit for measuring angles.
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A unit for measuring angles.
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degree
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Number of degrees in a circle.
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360
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360
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Number of degrees in a circle.
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A half-rotation of rays...
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is all of the rays that correspond to a common protractor.
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is all of the rays that correspond to a common protractor.
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A half-rotation of rays...
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(protractor) coordinate
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The rays in a half-rotation can b numbered so that to every ray there corresponds exactly one real number called its...
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The rays in a half-rotation can b numbered so that to every ray there corresponds exactly one real number called its...
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(protractor) coordinate
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The Protractor Postulate
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The rays in a half-rotation can be numbered from 0 to 180 so that positive number differences measure angles.
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The rays in a half-rotation can be numbered from 0 to 180 so that positive number differences measure angles.
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The Protractor Postulate
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If an angle is acute...
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then it is less than 90°. |
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If an angle is right...
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then it is 90°. |
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If an angle is obtuse...
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then it is more than 90° but less than 180°.
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If an angle is straight...
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then it is 180°.
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If an angle is less than 90°
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then it is acute.
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If an angle is is 90°
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then it is right.
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If an angle is is more than 90° but less than 180°.
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then it is obtuse...
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If an angles is is 180°
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then it is straight...
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Betweenness of Rays definition
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A ray is between two others in the same half-rotation iff its coordinate is between their coordinates.
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A ray is between two others in the same half-rotation iff its coordinate is between their coordinates.
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Betweenness of Rays definition
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Betweenness of Rays Theorem
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If OA - OB - OC, then ∠AOB + ∠BOC = ∠AOC
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If OA - OB - OC, then ∠AOB + ∠BOC = ∠AOC
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Betweenness of Rays Theorem
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Definition of midpoint of a line segment.
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A point is the midpoint of a line segment iff it divides the line segment into two equal segments.
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A point is the midpoint of a line segment iff it divides the line segment into two equal segments.
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Definition of midpoint of a line segment.
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A line bisects an angle iff it divides the angle into two equal angles.
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Definition of angle bisector.
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Definition of angle bisector.
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A line bisects an angle iff it divides the angle into two equal angles.
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congruent (‘con-GREW-ent’) |
Informally, same size, same shape, and referencing polygons or more complex figures. Line segments or angles the same size are ‘equal’, but triangles may be congruent. |
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Informally, same size, same shape, and referencing polygons or more complex figures |
congruent (‘con-GREW-ent’) |
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A theorem that can be easily proved as a consequence of a postulate or another theorem.
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corollary (‘COR-oh-lair-ee’)"
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corollary (‘COR-oh-lair-ee’)
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A theorem that can be easily proved as a consequence of a postulate or another theorem.
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Corollary to the Ruler Postulate
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A line segment has exactly one midpoint.
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A line segment has exactly one midpoint.
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Corollary to the Ruler Postulate
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An angle has exactly one ray that bisects it.
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Corollary to the Protractor Postulate.
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Corollary to the Protractor Postulate.
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An angle has exactly one ray that bisects it.
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Two angles are complementary...
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...iff their sum is 90°
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If the sum of the measures of two angles is 90° |
then the angles are complementary.
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Two angles are supplementary...
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...iff their sum is 180°
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If the sum of the measures of two angles is 180°
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then the angles are supplementary.
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Complementary angle theorem.
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Complements of the same angle are equal.
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Complements of the same angle are equal.
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Complementary angle theorem.
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Supplements of the same angle are equal.
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Supplementary angle theorem.
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Supplementary angle theorem.
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Supplements of the same angle are equal.
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Two angles are a linear pair...
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...iff they have a common side and their other sides are opposite rays.
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If two angles have a common side and their other sides are opposite rays...
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then the two angles are a linear pair.
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If the sides of one angle are opposite rays to the sides of the other...
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then the two angles are vertical angles.
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Two angles are vertical angles...
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...iff the sides of one angle are opposite rays to the sides of the other.
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Theorem: The angles in a linear pair ...
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...are supplementary angles.
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Theorem: Vertical angles ...
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... are equal angles.
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... iff they form a right angle.
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Two lines are perpendicular...
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Two lines are perpendicular...
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... iff they form a right angle.
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Complements of the same angle are... |
equal. |
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Supplements of the same ante are... |
equal. |
