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Chapter 3: Postulates, Theorems, and Corollaries
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Corresponding angle Postulate
If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent
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Alternate interior angle theorem
If 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent
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Same side interior angle theorem
If 2 parallel lines are cut by a transversal, then the same side interior angles are supplementary
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Alternate exterior angle theorem
If 2 parallel lines are cut by a transversal, then the alternate exterior angles are congruent
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Same side exterior angle theorem
If 2 parallel lines are cut by a transversal, then the same side exterior angles are supplementary
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Perpendicular transversal theorem
If a transversal is perpendicular to 1 of 2 parallel lines then it is perpendicular to the other
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Converse of the Corresponding angle Postulate
If 2 lines are cut by a transversal and the corresponding angles are congruent, the then lines are parallel
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Converse of the Alternate interior angle theorem
If 2 line are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel
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Converse of the same side interior angle theorem
If 2 line are cut by a transversal and the same side interior angles are supplementary, then the lines are parallel
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Converse of the alternate exterior angle theorem
If 2 line are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel
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Converse of the same side exterior angle theorem
If 2 line are cut by a transversal and the same side exterior angles are supplementary, then the lines are parallel
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Converse of the perpendicular transversal theorem
In a plane, 2 lines perpendicular to the same line, are parallel
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Parallel postulate
Given a line and a point not on that line, there is exactly 1 line THROUGH THE POINT parallel to the given line
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Perpendicular postulate
Given a line and a point not on that line, there is exactly 1 line THROUGH THE POINT perpendicular to the given line
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Theorem 3-10 (parallel transitive)
2 lines parallel to the same line, are parallel to each other
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Triangle exterior angle theorem
The measure of an exterior angle in a triangle is equal to the sum of the remote INTERIOR angles
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Interior angle sum theorem
The sum of the measures of the interior angles of a CONVEX polygon is (n - 2)*180
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Exterior angle sum theorem
The sum of the measures of the exterior angles of a polygon is 360 degrees
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Triangle ANGLE SUM theorem
The sum of the measures of the angles of a triangle equals 180 degrees
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Describe corollaries
A statement that follows readily after a theorem
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3rd angle corollary (tri.
If 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the 3rd angles are congruent
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Corollary 2 (tri.
Each angle of angle equiangular triangle has a measure of 60 degrees
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Corollary 3 (tri.
In a triangle, there can be AT MOST 1 right or 1 obtuse angle
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Corollary 4 (tri.
The acute angles of a right triangle are complementary
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