math postulates theorems and corollaries
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- Theorem 10
- If two angles of a triangle are equal the sides opposite them are also equal
- Theorem 7
- Perpendicular lines form right angles
- Theorem 15
- The triangle Inequality Theorem the sum of any two angles in triangle is greater than the third side
- Corollary 2 (T17)
- Supplementary interior angles on the same side of a transversal mean that lines are parallel
- Corollary 1 (T19)
- Parallel lines form equal alternate interior angles
- Theorem (Area)
- If the radius of a circle is r is area is ∏r squared
- Postulate 6 (SAS)
- If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent
- Corollary 1 (T17)
- Equal alternate interior angles mean that lines are parallel
- Corollary (equi...)
- an equiangular triangle is equilateral
- Theorem 9
- If two sides of a triangle are equal the sides opposite them are also equal
- Theorem (Circumference)
- If the diameter of a circle is d, its circumference is ∏d
- Theorem 12 (the exterior angle theorem)
- An exterior angle of a triangle is greater than either remote interior angle
- Postulate 5 (ASA)
- if two angles and the included of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent
- Theorem 14
- If two angles of a triangle are unequal the sides opposite them are also unequal in the same order
- Theorem 8
- If the angles in a linear pair are equal then their sides are perpendicular
- Corollary 3 (T19)
- in a plane a line perpendicular to one of two parallel lines is also perpendicular to each other
- Corollary definition of right angles
- all right angles are equal
- Theorem 18
- In a plane two lines parallel to a third line are parallel to each other
- Corollary to the ruler postulate
- A line segment has exactly one midpoint
- Postulate 2
- three non-collinear points determine a plane
- Postulate 7 (the parallel postulate)
- Through a point not on a line there is exactly one line parallel to the given line
- Corollary 2 (T19)
- Parallel lines form supplementary interior angles on the same side of a transversal
- Theorem 6
- Vertical angles are equal
- Postulate 3 (The ruler postulate)
- The points on a line can be numbered so that positive number differences measure distances.
- Theorem 1 (Betweenness of points theorem)
- If A-B-C then AB+BC=AC
- Corollary to the definition of the congruent triangles
- Two triangles are congruent to a third triangle are congruent to each other
- Pythagorean theorem
- the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two side
- Theorem 3
- Complements of the same angle are equal
- Theorem 19
- Parallel lines form equal corresponding angles
- Theorem 16
- in a plane two points each equidistant from endpoints of a line segment determine the perpendicular bisector of the line segment
- Corollary 3 (T17)
- in a plane two lines perpendicular to a third line are parallel
- Postulate 1
- two points determine a line
- Theorem 13
- If two sides of triangle are unequal the angles opposite them are also unequal in the same order
- Theorem 17
- Equal corresponding angles mean that lines are parallel
- Postulate 4 (The Protractor Postulate)
- The rays in a half-rotation can be numbered from 0-180 so that the positive number differences measure angles
- Corollary to the Protractor Postulate
- An angle has exactly one ray that bisects it
- Corollary (equi...)
- an equilateral triangle is equiangular
- Theorem 2 (Betweenness of rays theorem)
-
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- Theorem 11 (SSS)
- If three sides of one triangle are equal to the three sides of another triangle the triangles are congruent
- Triangle Angle Sum Theorem
- the sum of the angles of a triangle is 180
- Theorem 4
- Supplements of the same angle are equal
- Theorem 5
- The angles in a linear pair supplementary