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Math Theorems & Postulates

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vociyeme's version from 2017-10-14 13:37

Triangles, Segments, and Properties

Question Answer
Segment Addition PostulateIf 3 points A B and C are collinear and B is between A and C, the AB + BC = AC
Angle Addition PostulateIf point B is in the interior of angle AOC, then angle AOB + BOC = AOC and if AOC is a straight angle, then AOB + BOC = 180.
Reflexive PropertyIf line AB is congruent to line AB then angle A is congruent to angle A
Symmetric PropertyIf line AB is congruent to line CD then line CD is congruent to line AB
Transitive PropertyIf line AB is congruent to CD and CD is congruent to EF then line AB is congruent to line EF
Vertical Angles TheoremVertical angles are congruent.
Congruent Supplements TheoremIf two angles are supplements of congruent angles, then two angles are congruent
Congruent Complements TheoremIf two angles are complements of congruent angels, then the 2 angles are congruent
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Points of a Triangle

Bisector Theorems

Question Answer
Triangle Midsegment TheoremIf a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and half its length
Triangle Inequality TheoremThe sum of the lengths of any two sides of a triangle is greater than the length of the third side
Perpendicular Bisector TheoremIf a point is on the perpendicular bisector of a segment, then it is equidistant from the enpoints of the segment
Converse of Perpendicular Bisector TheoremIf a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment
Angle Bisector TheoremIf a point is on the angle bisector of an angle, then it is equidistant from the sides of the angle
Converse of Angle Bisector TheoremIf a point is equidistant from the sides of an angle, then it is on the angle bisector.
Hinge Theorm*If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is greater than the included angle of the second triangle, then the third side of the first triangle is greater than the third side of the second triangle.
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Circle Theorems

Question Answer
Equation of a CircleThe standard of an equation of a circle with center (h,k) and radius "r" is (x-h)2 + (y-k)2 = r2
Theorem 12-2If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.
Converse of Theorem 12-2If a line in the same plane as a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle.
Theorem 12-4Two segments tangent to a circle from a point outside the circle are congruent.
Theorem 12-5In the same circle or in congruent circles, (l) congruent central angles have congruent arcs, and (2) congruent arcs have congruent central angles
Theorem 12-6In the same circle or in congruent circles, (1) congruent chords have congruent arcs, and (2) congruent arcs have congruent chords.
Theorem 12-7A diameter that is perpendicular to a chord bisects the chord and its arc.
Theorem 12-8The perpendicular bisector of a chord contains the center of the circle.
Theorem 12-9In the same circle or in congruent circles, (1) chords equidistant from the center are congruent, and (2) congruent chords are equidistant from the center
Inscribed Angle TheoremThe measure of an inscribed angle is half the measure of its intercepted arc
Theorem 12-11The measure of an angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc.
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