Geometry First semester
Terms
undefined, object
copy deck
- Collinear
- lies on the same line
- Noncollinear
- not on the same line
- Planes
- flat surface that extends indefinitely in all directions. represented by a capitol script letter or 3 pts on teh plane
- Line
- extends undefinitely in 2 directions
- Segment Addition
- adding of two parts of a line or two separate lines
- Pythagorean Theorem
- a^2+b^2=c^2
- congruent
- =
- Segment bisector
- a segment, line, or plane that intersects a segment at its midpoint
- theorems
- a statement that can be proved to appeal to postulates, definations, algebraic properties or rules of logic
- Angle
- a figure consisting of 2 noncollinear rays with a common endpoint
- Ray
- starts at a point and continues in one direction forever
- Opposite rays
- 2 rays <a---b---c> such as ba and bc
- sides
- in an angle the 2 sides that formthe angle, or a segment joining 2 consecutive vertices of the polygon
- Vertex
- the common endpoint in a ray, the connection of 2 sides
- Degrees
- unit of measure for angles and arcs
- measure
- length AB written without the line above it
- Right angle
- 90 degrees
- Acute angle
- less than 90
- Obtuse angle
- greater than 90
- angle bisector
- splits angle into 2 even parts
- perpendicular lines
- form 90 degree angle
- adjacent angle
- have a common endpoint and a common side but no common interior sides
- Verticle angle
- 2 non adjacent angles formed by 2 intersecting lines
- linear pair
- pair of adjacent angles whose noncommon sides are opposite rays
- Supplementary
- 2 angles whos measures add to 180
- Complimentary
- angle measures add to 90
- Inductive Reasoning
- Reasoning uses a number of specific examples to arrive at a plausible generalization or prediction. Conclusions arrived at by inductive reasoning lack the logical certainty of those arrived at by deductive reasoning
- Counterexample
- shows the given statement is not always true
- If-then statements
- compound statement "if A, then B" where A and B are statements
- Conditional Statemetn
- A statement in If-then form. If is the hypothesis and then is the conclusion
- Hypothesis
- in a conditional statement this immediately follows the if
- Conclusion
- the part following the word then in an if-then statement
- Converse
- p->q
- Negation
- denial of a statement
- inverse
- ~p->~q
- contrapositive
- ~q->~p
- Deductive reasoning
- system of reasoning to reach conclusions which must be true when the assumptions on which the reasoning is based is true
- law of detatchment
- in a true p->q if p is true then q is true
- law of syllogism
- if p->q and q->r are true then p->r is also true
- parallel lines
- lines in the SAME PLANE that dont intersect
- skew lines
- lines that dont intersect but lie in DIFFERENT planes
- transversal
- a line that intersects 2 or more lines in a plane at different points
- CIA
- consecutive interior angles are supplementary if 2 Parallel lines are cut by a transversal
- AIA
- alternate interior angles congruent
- AEA
- also congruent
- CA
- corresponding congruent
- Slope
- (y2-y1)/(x2-x1)
- If and only if
- when both conditional and converse are true
- Spherical Geometry
- branch of geometry that dals with a system of points, great circles (lines), and spheres (planes)
- Great Circle
- for a given sphere, the intersection of the sphere and a plane taht contains the center of the sphere
- Arc
- an unbroken part of a circle
- Traingle
- segments connecting 3 noncollinear points, has 3 parts:interior, exterior, trinagle itself
- Polygon
- a figure in a plane that meets the conditions: closed and formed by 3 or more coplanar segments, sides that have a common ednpoint are noncollinear, each side intersects exactly 2 other sides but only at endpoints
- Acute tringle
- a triangle all of whose angles are acute
- Obtuse triangle
- has one obtuse angle
- right triangle
- has one right angle
- equilateral
- 3 congruent sides
- Scalene
- no congruent sides
- Isosceles triangle
- 2 congruent sides and 2 congruent angles ITT
- Equiangular Triangle
- All angles congruent
- Base angles
- in an isoceles triangle the angle formed by the base and one of the legs
- Triangle sum
- 180
- Auxiliary line
- a line or segment added to a given figure to help in proving a result
- Congruent Triangles
- Traingles with corresponding parts congruent
- CPCTC
- Congruent parts of congruent triangles are congruent (must prove triangles congruent first)
- Included angle
- angle formed by 2 sides of a triangle is the inclueded angle for those 2 sides
- SSS
- 3 sides congruent to corrseponding sides on antoher triangle
- SAS
- side angle side
- ASA
- angle side angle
- AAS
- angle angle side
- ITT
- Isoceles traingel theorem, 2 sides of triangle congruent then the angles opposite the sides are congruent
- Perpendicular Bisector
- a bisector of a segment that is perpedicular to the segment
- median
- ina triangle, a segment joins the median of a side and the opposite point
- altitude
- a segment from the vertex of the triangle to the line containing the opposite side and perpendiular to the line containing that side
- LL
- in a right triangle prove conguent by Leg leg
- HA
- in a right triangle proving congruent by using the hypotenuse and a acute angle of the triangel
- LA
- in a right triangle uses on leg and an acute angle of the triangle
- HL
- in a right triangle uses the hypotenuse and the leg
- indirect proof
- proof by contradiction
- EAT
- measure of an exterior angle is greater than the sum of the two remote interior angles
- quadrilaterals
- 4 sided polygon
- parallelogram def
- both pairs of opposite sides parallel
- properties of parallelogram
- opp. sides congruent, opp. angles congruent, consecutive angles supplementary, diagonals bisect eachother
- rectangle def
- a quad with four right angles
- prop of a rectangle
- opp. sides parallel and congruent, opp angles congruent, consec angles supplementary, diagonals bisect and are CONGRUENT
- rhombus def
- a quad with 4 congruent sides
- prop of a rhombus
- diagonals are PERPENDICULAR, diagonals bisect opp angles and opp angles are congruent
- square
- a quad that is a rectangle and rhombus
- Trapezoid def
- a quad with exactly 1 pair of parallel sides
- isoceles trapezoid
- has congruent legs
- iscoeles trap. prop
- diagonals are congruent but dont bisect, midsegment of a trap is the average of base lengths