Theorem/Postulate Flashcards
About this set
Created by:
KateBell44 on December 11, 2010
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Description:
This is just a rough list of theorems we've covered from chapter 1 to chapter 5. Hope it helps!
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37 terms
Terms | Definitions |
|---|---|
 segment addition postulate | AB + BC = AC |
| Linear Pair Postulate | m<1 + m<2= 180 degrees |
| Vertical Angles Theorem | If two angles intersect to form an X, the non adjacent angles are congruent |
| Angle Addition Postulate | if point B lies in the interior of <AOC then m<AOB+m<BOC=m<AOC |
| syllogism | p -> q, and q -> r, then p -> r |
| Detatchment | p -> q, p is true than q is true |
| Congruent Supplements Theorem | if m<1 + m<2=180, and m<2 + m<3 = 180, then m<1 + m<3 = 180. |
| Congruent Complements Theorem | if m<4 + m<5 = 90, and m<5 + m<6 = 90, then m<4 + m<6 = 90. |
| reflexive property | a=a |
| Symmetric Property | ab=ba |
| Transitive Property | ab=cd, cd=ef, then ab=ef |
| Parallel Postulate | If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given lines |
| Perpendicular Postulate | 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 |
| Theorem 3.3 | If two lines are perpendicular, then they intersect to for 4 right angles |
| 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 |
| Corresponding angles postulate | if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent |
| Alternate exterior angles postulate | if two lines cut by a transversal are parallel, then alternate exterior angles are congruent |
| Triangle Sum theorem | The 3 interior angles of a triangle add up to 180 degrees |
| Exterior angles theorem | 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 | If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent |
| Reflexive Propery (Triangles) | Every triangle is congruent to itself |
| Perpendicular Transversal | If a transversal is perpendicular to one of two parallel lines, then it is also perpendicular to the other |
| Base angles theorem (Converse) | If 2 <s of a Δ are ≅, then the 2 sides opposite are ≅ |
| Postulate/Slopes of Perpendicular Lines | Two lines are perpendicular is and only if the product of the slope is -1 |
| Side Side Side Postulate | If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent |
| Side Angle Side Postulate | If two sides and an included angle of one triangle are congruent to two sides and an included angle of a second triangle, then the two triangles are congruent |
| Angle Side Angle Postulate | If two angles and an included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent |
| Theorem 3.2 | If two sides of two adjacent acute angles are perpendicular, then the angles are complementary |
| Theorem 3.3 | If two lines are perpendicular, then they intersect to form 4 right angles |
| Perpendicular Travsversal Theorem | If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other |
| Theorem 3.11 | If two lines are parallel to the same line, then they are parallel to eachother |
| Theorem 3.12 | In a plane, if two lines are perpendicular to the same line, then they are parallel to eachother |
| Collorary to the triangle sum theorem | the acute angles of a triangle are complementary |
| Converse of the base angles theorem | If two angles of a triangle are congruent, then the sides opposite them are congruent |
| Collorary of the converse of the base angles theorem | If a triangle is equiangular then it is also equilateral |
| Hypotenuse-Leg Theorem | If they hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then those two triangles are congruent |
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