## Semester 1 Math Vocab/Theorems/Postulates/Corollaries

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izgiz22  on December 18, 2010

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# Semester 1 Math Vocab/Theorems/Postulates/Corollaries

 congruent objectstwo objects w/ the same size and shape
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#### Definitions

congruent objects two objects w/ the same size and shape
congruent segments segments with the same length
midpoint of a segment divides a segment in 2 congruent segments
bisector of a segment a line, segment, ray or object that intersect a segment at its midpoint
congruent angles angles w/ equal measures
adjacent angles 2 angles in a plane w/ a common vertex, a common side, but not a common exterior point.
bisector of an angle ray that divides an angle into 2 congruent angles
linear pair 2 angles that are adjacent and their non-common sides are opposite rays. the sum of the measure of the angles is 180.
converse if q, then p
biconditional a statement that contains the words "if and only if"
deductive reasoning proving statements by reasoning from accepted postulates, definitions, theorems and given information.
complementary angles two angles whose measures have the sum of 90.
supplementary angles two angles whose measures have the sum of 180.
vertical angles two angles such that the sides of the one angle are opposite rays to the sides of the other angle.
perpendicular lines two lines that intersect to form right angles (90)
skew lines noncoplanar lines. neither parallel nor intersecting
parallel planes planes that do not intersect
transversal a line that intersect two or more coplanar lines in different points.
auxiliary lines a line (or ray or segment) added to a diagram to help in a proof.
corollary a statement that can be proved easily by applying a theorem.
polygon a plane figure formed by coplanar segments (sides) such that (1) each segment intersects exactly two other segments, one at ach endpoint; and (2) no two segments with a common endpoint are collinear.
diagonal a segment joining to non-consecutive vertices of a polygon.
congruent figures when two figures have the same size and shape
congruent triangles two triangles that have vertices that can be matched up so that the corresponding parts (angles and sides) of the triangles are congruent.
congruent polygons two polygons that have vertices that can be matched up so that their corresponding parts are congruent.
legs of an isosceles triangle the congruent sides of an isosceles triangle
base of an isosceles triangle the third side of an isosceles triangle that is not congruent to any other side.
median of a triangle a segment from a vertex to the midpoint of the opposite side
altitude of a triangle the perpendicular segment from a vertex to the line that contains the opposite side.
perpendicular bisector a line (or ray or segment), that is perpendicular to the segment at its midpoint. In a given plane, there is exactly one line perpendicular to a segment at its midpoint.
parallelogram a quadrilateral with both pairs of opposite sides parallel.
rectangle a quadrilateral with four right angles. All are parallelograms.
rhombus a quadrilateral with four congruent sides. All are parallelograms.
square a quadrilateral with four right angles and four congruent sides. All are rectangles, rhombuses, and parallelograms.
Trapezoid a quadrilateral with exactly one pair of parallel sides.
Base of a trapezoid the parallel sides of a trapezoid
Legs of a trapezoid the other, non parallel sides of a trapezoid
isosceles trapezoid a trapezoid with congruent legs. both pairs of base angles are congruent.
median of a trapezoid a segment that joins the midpoint of legs of a trapezoid
mid-segment of a triangle the segment that joins the midpoints of the 2 sides of a triangle.
inverse if not p, then not q
contrapositive if not q, then not p.
logically equivalent statements statements that are either both true or both false.
ruler postulate 1. the points on a line can be paired with the real numbers
2. the distance between any two points equals the absolute value of the difference of their coordinates.
segment addition postulate if B is between A and C, then AB + BC = AC
angle addition postulate If point B lies in the interior of angleAOC, then the measure of angleAOB+angleBOC=the measure of angleAOC.
midpoint theorem if M is the midpoint of segmentAB, then AM=1/2AB and MB=1/2AB.
Angle bisector theorem if rayBX is the bisector of angleABC, then measure of angleABX=1/2measure of angleABC and measure of angleXBC =1/2 measure of angleABC.
If two lines are perpendicular... they form congruent adjacent angles
Two lines parallel to a third line... are parallel to each other
If two angles of one triangle are congruent to two angles of another triangle... then the third angles are congruent.
The sum of the interior angles of a quadrilateral... is 360
the acute angles of a right triangle... are complimentary
The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is... 360
the segment that joins the midpoints of two sides of a triangle... 1. is parallel to the third side
2. is half as long as the third side
the diagonals of a rectangle... are congruent
the diagonals of a rhombus... are perpendicular
a line that contains the midpoint of one side of a triangle and is parallel to another side... passes through the midpoint of the third side
the midpoint of the hypotenuse of a right triangle... is equidistant from the three vertices
if an angle of a parallelogram is a right angle... then the parallelogram is a rectangle
if two consecutive sides of a parallelogram are congruent... then the parallelogram is a rhombus
the median of a trapezoid... 1. is parallel to the bases
2. has a length equal to the average of the base lengths.

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