# Geometry_Honors_Midterm.txt

 undefined terms can not be defined using other figures. PointLinePlane Point names a location and has no size. it is represented by a dot. A capital letter Line a straight path that has no thickness and extends forever A lower case letter or two points on the line Plane a flat surface that has no thickness and extends forever.a script capital letter or three points not on a line. collinear points that lie on the same line noncollinear points that do not lie on the same line line segment the part of a line consisting of two points and all points between them endpoint a point at one end of a segment or the starting point of a ray A capital letter ray part of a line that starts at an endpoint and extends forever in one direction It's endpoint and any other point Opposite Rays two rays that have a common endpoint and form a line postulate a statement that is accepted as true without proof intersection the set of all points the two or more figures have in common system of equations a set of two or more equations containing two or more of the same variables coordinate a number used to identify the location of a point distance between any two points the absolute value of the difference of the coordinates length of AB the distance between A and B Finding the Length of a Segment | a-b | or | b-a | congruent segments segments that have the same length uses tick marks midpoint the point that bisects, or divides the segment into two congruent segments segment bisector any ray, segment, or line that intersects a segment at its midpoint angle a figure formed by two rays, or sides, with a common endpoint vertex a common endpoint How to name an angle Vertexa point on each ray and the vertexnumber interior of an angle the set of all points between the sides of the angle exterior of an angle the set of all points outside the angle the measure of an angle the absolute value of the difference of the real numbers that the rays correspond with on a protractor Acute Angle measures greater than 0 degrees and less than 90 degrees Right Angle Measures 90 degreesmust have box obtuse angle measures greater than 90 degrees and less than 180 degrees straight angle formed by two opposite raysmeasures 180 degrees congruent angles angles that have the same measure angle bisector a ray that divides an angle into two congruent angles the (particular points) of all points in the interior of the angle that are equidistant from the sides of the angle Adjacent Angles two angles in the same plane with a common vertex and a common side, but no common interior points linear pair of angles a pair of adjacent angles whose noncommon sides are opposite rays complementary angles two angles whose measures have a sum of 90 degrees supplementary angles two angles whose measures have a sum of 180 degrees Finding the Complementary angle 90-x finding the supplementary angke 180-x vertical angles two nonadjacent angles formed by two intersecting lines perimeter the sum of the side lengths of the figure rectangle- 2l+2wsquare- 4striangle a+b+c area the number of non overlapping square units of a given size that cover the figure rectangle- l*wSquare side squaredTriangle- 1/2bhcircle- pi(r) squared base of a triangle any side of a triangle height a segment from a vertex that forms a right angle with a line containing the base may be:inside the triangle (interior)outside (exterior)a side of the triangle diameter a segment that passes through the center of the circle and whose endpoints are on the circle radius a segment whose endpoints are the center of the circle and a point on the circle circumference the distance around a circle c=pi(d) or 2pi(r) pi irrational 3.14 or 22/7 coordinate plane a plane that is divided into 4 regions by the x and y axis Midpoint formula m= (x1+x2 / 2, y1+y2 /2) distance formula d= square root of (x2-x1)2 + (y2-y1)2 pythagorean theorem ONLY in a right triangleused to find distancea2+b2=c2 legs of a right triangle the 2 sides that form the right angle hypotenuse the side across from the right triangle that stretches from one leg to the other transformation a change in the position, size, or shape of a figure preimage the original figure image the resulting figure ---> arrow notation used to describe a transformation ' primes used to label the image reflection (flip) a transformation across a line, called the line of reflection. each points and its image are the same distance from the line of reflection Rotation (turn) a transformation about a point P, called the center of rotation. Each point and its image are the same distance from P Translation (slide) a transformation in which all the points of a figure move the same distance in the same direction inductive reasoning the process of reasoning that a rule or statement is true because specific cases are true used to draw a conclusion from a pattern 1) look for a pattern2) Make a conjecture3) prove the conjecture or find a counterexample conjecture a statement believed to be true based on inductive reasoning counterexample an example that proves a conjecture false conditional statement a statement that can be written in the form "if p, then q" p--> q hypothesis the part of p of a conditional statement following the word "if" conclusion the part q of a conditional statement following the word, "then" truth value true or false of a conditional statement false when the hypothesis is true and the conclusion if false negation of statement p (opposite) ~p the negation of a true statement is false, the negation of a false statement is true converse statement formed by exchanging the hypothesis and conclusion q-->p inverse statement formed by negating the hypothesis and the conclusion ~p--> ~q contrapositive statement formed by both exchanging and negating the hypothesis and conclusion ~q --> ~p logically equivalent statements related conditional statements that have the same truth value deductive reasoning process of using logic to draw conclusions from given facts, definitions, and properties biconditional statement a statement that can be written in the form, "p if and only if q" (iff) if p, then q if q, then p used to write defintions definition a statement that describes a mathematical object and can be written as a true biconditional iff polygon closed plane figure formed by 3 or more line segments each segment intersects exactly two other segments only at their endpoints no two segments with a common endpoint are collinear triangle a three sided polygon quadrilateral a 4 sided polygon proof an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true theorem any statement that you can prove two column proof proof that lists the steps of the proof in the left column and the matching reason in the right column. proof process 1) write the conjecture to be proven 2) draw a diagram to represent the hypothesis of the conjecture 3) state the given information and mark it on the diagram 4) state the conclusion of the conjecture in terms of the diagram 5) plan your argument and prove the conjecture flow chart proof uses boxes and arrows to show the structures of the proof moves from left to right or top to bottom justification written below the box paragraph proof presents the steps of the proof and their matching reasons as sentences in a paragraph parallel lines (||) coplanar and do not intersect perpendicular lines (upside down T) intersect at 90 degree angles. skew lines are not coplanar, are not parallel, and do not intersect parallel planes planes that do not intersect transversal a line that intersects two coplanar lines at two different points t other 2 lines = r and s corresponding angles lie on the same side of the transversal, on the same sides of lines r and s. alternate interior angles nonadjacent angles lie on opposite sides of the transversal t, between lines r and s alternate exterior angles lie on opposite sides of the transversal t outside lines r and s same-side interior angles (consecutive interior angles) lie on the same side of the transversal between lines r and s perpendicular bisector of a segment a line perpendicular to a segment at the segment's midpoint distance from a point to a line the length of the perpendicular segment from the point to the line rise the difference in the y values of the 2 points on a line run the difference in the x values of 2 points on a line slope the ratio of rise to run, m= y2-y1 / x2-x1 positive slope negative slope zero slope undefined slope opposite reciprocals a/b and -b/a point slope form of a line y-y1=m(x-x1) x1, y1 is a given point on the line slope intercept form y=mx+b m=slope b=y intercept the equation of a vertical line x=a a= x intercept equation of horizontal line y=b b= y intercept y=5x+8 y=5x-4 same slope, different y intercept acute triangle three acute sides equiangular triangle 3 congruent acute angles right triangle one right angle obtuse triangle one obtuse angle equilateral triangle three congruent sides isosceles triangle at least 2 congruent sides scalene triangle no congruent sides auxiliary line a line that is added to a figure to aid in a proof ----------- corollary a theorem whose proof follows directly from another theorem interior set of all points inside the figure exterior the set of all points outside the figure interior angle formed by 2 sides of a triangle exterior angle formed by one side of the triangle and the extension of an adjacent side remote interior angle an interior angle that is not adjacent to the exterior angle triangle rigidity if the side lengths of a triangle are given, the triangle can have only one shape. included angle an angle formed by two adjacent sides of a polygon included side the common side of 2 consecutive angles in a polygon coordinate proof uses coordinate geometry and algebra strategies for positioning figures in the coordinate plane use the origin as a vertex, keeping the figure in Quad I center the figure at the origin center a side of the figure at the origin use one or both axes as sides of the figure vertex angle angle formed by the legs base side opposite the vertex angle base angles 2 angles that have the base as a side equidistant a point is the same distance from 2 or more objects concurrent three or more lines intersect at one point point of concurrency the point where the lines intersect circumcenter of a triangle the point of concurrency in a triangle circumscribed a circle that contains all the vertices of a polygon incenter of the triangle the point of concurrency where the angle bisectors meet? (unsure) inscribed intersects each line that contains a side of the polygon at exactly one point incenter the center of the triangle's inscribed triangle always inside the triangle median of a triangle a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side each triangle has 3 medians, which are concurrent centroid of the triangle the point of concurrency of the medians of a triangle always inside the triangle center of gravity altitude of a triangle perpendicular segment from a vertex to the line containing the opposite side each triangle has 3 altitudes can be inside, out, or on the triangle the height of a triangle is the length of an altitude miscellaneous shit orthocenter of the triangle the point of intersection of the 3 altitudes of a triangle midsegment of a triangle segment that joins the midpoints if two sides of the triangle every triangle has 3 midsegments, qhich form the midsegment triangle indirect proof 1) identify the conjecture 2) assume the opposite of the conclusion is true 3) use direct reasoning to show that the assumption leads to a contradiction 4) conclude that since the assumption is false, the original conjecture is true Authorghstechnology ID82453 Card SetGeometry_Honors_Midterm.txt DescriptionGeometry honors Updated2011-04-28T12:07:37Z Show Answers