Semester 1 Math Vocab/Theorems/Postulates/Corollaries
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62 terms
Terms | 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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