Linear Pair Postulate If two angles form a linear pair, then the measures of the angles add up to 180°. “if and only if” “iff” Theorem 1.7: If two angles are complementary to the same angle (or to congruent angles) then these angles are congruent Theorem 1.7: If two angles are supplementary to the same angle (or to congruent angles, then the angles are congruent. Theorem 1.7: If two lines meet to form a right angle, then these lines are perpendicular.
Theorem 1.6: If two lines are perpendicular, then they meet to form right angles. Definition: “Officially”, Perpendicular lines are two lines that meet to form congruent adjacent angles. Postulate 9: If a point D lies in the interior of angle ABC, then m ABD + m DBC = m ABC Theorem 1.4: There is one and only one angle bisector for any given angle. Postulate 8: The measure of an angle is a unique positive number. Theorem 1: The midpoint of a line segment is unique. Postulate 6: If two planes intersect, then their intersection is a line.+ Postulate 7: If two points lie in a plane, then the line joining them lies in that plane. Postulate 3: If X is a point on AB and A-X-B (X is between A and B), then AX + XB = AB Postulate 4: If two lines intersect, then they intersect in exactly one point Postulate 5: Through any three noncollinear points, there is exactly one plane. The measure (or length) of AB is a positive number, AB. Postulate 2: The measure of any line segment is a unique positive number. GEOMETRY POSTULATES AND THEOREMS Postulate 1: Through any two points, there is exactly one line.
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