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| represents an infinite number of points that are arranged in a straight manner |
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| represents a flat surface that streches indefinitely in all directions. |
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| has three dimensions L-W-H |
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| only has two dimensions L-W |
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| consists of two endpoints and all the points on the line between them. |
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| consists of one endpoint and all the points on a line that lies on the same side of the line as another specified point. |
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| is used to describe segments of the same length or shapes that are the same size and shape. |
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| consists of two rays with a common endpoint. |
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| >90 degrees(between 90 and 180) |
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| <90 degrees(between 0-90) |
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| points that lie on the same plane |
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| points that lie on the same plane |
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| share a common vertex and side between the two noncommon sides |
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| are non-adjacent angles formed by two intersecting lines |
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| are ones whose angles add up to a sum of 180 degrees. |
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| are angles whose measures add up to 90 degrees. |
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| a line that passes through the midpoint of a segment and is perpendicular to the line segment. |
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| also called axiom. This is an accepted statement of fact. |
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| are two collinear rays with the same endpoint. |
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| are lines that never intersect and are next to each other. |
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| are noncoplanar, they don't intersect nd are not parallel. |
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| are planes that don't intersect. |
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| is the process of observing, recognizing, and describing patterns and then making predictions or generalizations for thoses patterns. |
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| is what the predictions and generalizations are called. |
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| is the process of using facts tht are accepted as true to demonstrate the truth of other statements. |
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| is anything that dits the conditions specified in a conjecture but does not satisfy it's conclusion. |
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| normally begins logical statements. This is a statement that relates two ideas with an "if-then" conjunction. |
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| a variation of a conditional statement. this is written by negating the "if and then" parts of the statement. |
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| is a variation of a conditional statement This is written by reversing the "if" and "then" parts of a statement. |
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| is written by negating and reversing the "if" and "then" parts of the statement. This is a type of variation of a conditional statement. |
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| The Law of Contrapositives |
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| states that if a conditional statement is true, then it's contrapositive will be true as well. |
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a formal argument that shows how a set of premises logicallyy leads to a desired conclusion
shown in three ways
paragraph form
flow charts
two column proof(look at notes) |
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is a type of geometry that came as a result of the changing of the fifth postulate to " Given a line and a point not on that line there are at least two lines through the given point parallel to the given line."
it used to be "Any two lines always intersect" |
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| is a line that intersects two or more coplanar lines at distinct points. |
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| two lines intersected by a transversal are parallel if and only if alternate interior angles are congruent. |
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| two lines intersected by a transversal are parallel if and only if corresponding angles are congruent |
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| two lines intersected by s transversal are parallel if and only if alternate exterior angles are congruent. |
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| Two Lines intersected by a transversal are parallel if and only if interior angles on the same side of the transversal are supplementary. |
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| If two lines are perpendicular to the same line, then they are parallel to each other. |
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| is a proof where arrows show the logical connections between the statements |
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| consists of three segments determined by three non-collinear points as their endpoints. |
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| has three congruent sides |
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| when all three angles of a triangle have the same measure |
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| The sum of the measures of a triangle is 180 degrees |
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| If two angles of one triangle are congrent to two angles of a second triangle then the third angles must also be congruent. |
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| is an angle that makes a linear pair with one of the angles of the triangle. |
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| are the angles not adjacent to the exterior angle |
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| The measure of an exterior angle of a triangle equals the sum of the measures of it's two remote interior angles. |
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| is the distance around it's sides or the sum of the lengths of the three sides |
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| have corresponding angles and corresponding sides that are congruent |
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| two triangles are congruent if two angles and one sidee of the triangle are congruent to the corresponding angles and side of the second. |
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| two triangles are congruent if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of the second. |
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| two triangles are congruent if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of the second. |
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| two triangles are congruent if all three sides of the one triangle are congruent to the corresponding sides of the second. |
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| A triangle is isosceles if nd only if the angles opposite the congruent sides are also congruent. |
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| A triangle is equilateral if and only if it is equiangular. |
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| Each angle of an equilateral triangle measures 60 degrees. |
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| is a segment from a vertex of the triangle, perpendicular to a line containing the opposite side of the triangle. |
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| an altitude of an equilateral triangle is also a median. |
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| is the union of three or more coplanar segments in which exactly two segments intersect at each edpoint. |
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| is a segment containing any two nonconsecuetive vertices of the polygon. |
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| is a polygon where all diagonals lie completely within the polygon. |
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| has at least one diagonal that lies outside the polygon. |
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| The sum of the measures of the interior angles of a convex polygon is 180(n-2) |
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| The sum of the measures of the exterior angles, one at each vertex, for any convex polygon is 360 degrees. |
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| is a polygon where all sides are congruent |
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| is a polygon where all interior angles are congruent. it is impossible for a concave polygon to be equiangular |
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| is a polygon that is both equilateral and equiangular. |
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| Every interior angle of a regular n-gon measures 180(n-2) divided by n. |
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| Every exterior angle of a regular n-gon measures 360 degrees divided by n. |
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is a polygon that has four sides
has four interior angles |
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| are two sides in a quadrilateral that share a common vertex |
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| are sides that do not intersect |
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| don't share a common side |
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| are quadrilaterals with two pairs of parallel opposite sides |
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| is a quadrilateral with one pair of parallel opposite sides |
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| opposite sides of a parallelogram are congruent |
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| Opposite angles of a parallelogram are congruent |
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| Diagonals of a parallelogram bisect each other |
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| A quadrilateral is a parallelogram if and only if both pairs of opposite sides are congruent |
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| A quadrilateral is a parallelogram if and only if both pairs of opposite angles are congruent |
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| A quadrilateral is a parallelogram if and only if it contains a pair of parallel opposite sides which are congruent |
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| A quadrilateral is parallelogram if and only if its diagonals bisect each other. |
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| an equiangular polygon, each angle of a rectangle equals 90 degrees. The diagonals of a rectangle are congruent |
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| A parallelogram is a rectangle if and only if it's diagonals are congruent |
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| is the equilateral quadrilateral. diagonals of this shape bisect each other and each vertices are equidistant from the other diagonal diagonals of this shape are perpendicular bisectors. |
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| A parallelogram is a rhombus if its diagonals are perpendicular. |
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| is the shape that is both equilateral and equiangular- square |
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| is a shape that is a special rectangle(because it's equiangular) and a special rhombus(because it's equilateral). it's diagonals are congruent. |
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| is a shape that has a pair of opposite sides that are parallel. the other pair of opposite sides are not parallel. parallel sides= bases not parallel sides=legs |
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| is any segment from one base of the trapezoid to the other base that is perpendicular to the bases. |
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| The median of a trapezoid is parallel to it's bases. |
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| The length of the median of a trapezoid is half the sum of the lengths of it's bases |
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| is a trapezoid with congruent legs. |
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| A trapezoid is isosceles if and only if it's base angles are congruent |
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| A trapezoid is isosceles if and only if it's diagonals are congruent. |
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