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44 Cards in this Set

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P1 Ruler Postulate
Distance between points A and B is the absolute value of the difference between the coordinates of A and B. (A ruler can measure this distance)
P2 Segment Addition Postulate
AB + BC = AC (If B is between A and C)
P3 Protractor Postulate
A protractor can measure the angle between two rays with a shared initial point
P4 Angle Addition Postulate
If P is in the interior of ∠RST then m∠RSP + m∠PST = m∠RST
P5 Through any two points...
Through any two points there exists exactly one line
P6 A line contains at least ___ points
A line contains at least two points
P7 If two lines intersect, the intersection is a ______
If two lines intersect, the intersection is a point
P8 Through any three non-collinear points, there exists _____
Through any three non-collinear points, there exists exactly one plane
P9 A plane contains at least _____
A plane contains at least three non-collinear points
P10 If two points lie in a plane, then the line containing them _____
If two points lie in a plane, then the line containing them lies in the plane
P11 If two planes intersect, the intersection is a ______
If two planes intersect, the intersection is a line
Properties of Segment Congruence Theorems (three)
Reflexive: AB≅AB | Symmetric: AB≅CD ⇔ CD≅AB | Transitive: If(AB≅CD and CD≅EF) then (AB≅EF)
Properties of Angle Congruence Theorems (three)
Reflexive: ∠A≅∠A | Symmetric: ∠A≅∠B ⇔ ∠B≅∠A | Transitive: If(∠A≅∠B and ∠B≅∠C) then (∠A≅∠C)
Right Angle Congruence Theorem
All right angles are congruent
P12 Linear Pair Postulate
If two angles form a linear pair, then they are supplementary (180°)
Congruent Supplements Theorem
If two angles are supplementary the the same angle then they are congruent
Congruent Complements Theorem
If two angles are complementary to the same angle, then they are congruent
Vertical Angles Theorem
Vertical Angles are congruent
P13 Parallel Postulate || (point and line)
If there is a line and a point not on the line, then there is one line through the point parallel(||) to the given line
P14 Perpendicular Postulate ⊥ (point and line)
If there is a line and a point not on the line, then there is exactly one line through the point perpendicular(⊥) to the given line.
If two lines intersect to form a linear pair of congruent angles, then the lines are _____
If two lines intersect to form a linear pair of congruent angles, then the lines are PERPENDICULAR
If two sides of two adjacent acute angles are perpendicular, then the angles are _______
If two sides of two adjacent acute angles are perpendicular, then the angles are COMPLEMENTARY
If two lines are perpendicular, then they intersect to form four ______
If two lines are perpendicular, then they intersect to form four RIGHT ANGLES
P15 Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary
Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other
P16 Corresponding Angles Converse
If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel
Alternate Interior Angles Thm Converse
If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel
Consecutive Interior Angles Thm Converse
If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel
Alternate Exterior Angles Thm Converse
If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel
If two lines are parallel to the same line, then they are ____ to each other
If two lines are parallel to the same line, then they are parallel to each other
In a plane, if two lines are perpendicular to the same line, then they are ______ to each other
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other
P17 Slopes of Parallel Lines
Two lines are parallel if and only if they have the same slope (or are both vertical)
P18 Slopes of Perpendicular Lines
Two nonvertical lines are perpendicular if and only if the product of their slopes is -1 (negative reciprocals). Vertical and horizontal lines are perpendicular
Triangle Sum Theorem (& corollary for right angles)
The sum of the measures of the interior angles of a triangle is 180° | Corollary - the acute angles of a right triangle are complementary
Exterior Angle Theorem (for triangles)
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles
Third Angles Theorem
(for triangles)
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. (180° - ∠A - ∠B) = ∠C
Properties of Congruent Triangles Theorem (three)
Reflexive: Every triangle is congruent to itself | Symmetric: if (∆ABC≅∆DEF) then (∆DEF≅∆ABC) | Transitive: if (∆ABC≅∆DEF and ∆DEF≅JKL) then (∆ABC≅∆JKL)
P19 SSS Congruence Postulate
If three sides of a triangle are congruent to three sides of a second triangle, then the two triangles are congruent
P20 SAS Congruence Postulate
If two sides and the included angle of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent
P21 ASA Congruence Postulate
If two triangles and the included side of one triangle are congruent to two angles and the included side of a second triangle, the two triangles are congruent. (Also called ASAA or AAAS, can you see why?)
AAS Congruence Theorem
If two angles and the nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent.
This can also be called AAAS or ASA, can you see why?