Download Comprehensive List of First Semester Theorems All radii of

Comprehensive List of First Semester Theorems
All radii of a circle are congruent
Linear Pair Theorem
Diameter  2(radius)
Bisectors of L.P  Perp
Adj angles w/ perp noncommon rays  complementary
Congruent Complement
Congruent supplement
Vertical Angle Theorem
Outer segment/angle congruent  Overlapping seg/angle congruent
2 perpendicular lines  4 90 degree angles, 4 rt angles, 4 cong angles
Congruent L.P Theorem
ISO  BAM (*BMISO has NOT been proven)
Angle formed by bisect rt angle  45 degrees
Isosceles Theorem
Converse Isosceles Theorem
All right angles congruent
If multiple rays originate from same endpoint, sum of non overlapping angles is 360.
Point on perpendicular bisector  equidistant from segments endpoints
Whole is greater than part
Exterior Angle Theorem
Exterior Angle Sum Theorem
2 lines perp to the same line  ll
A 1st line ll to a 2nd line that is perp to a third  1st and 2nd perp
Cong corr. <’s  ll lines
Cong alt. int. <’s  ll lines
Cong s.s. supp <’s  ll lines
Given any point and any line, unique perpendicular
Midpoints are unique
Angle bisectors are unique
Perpendicular bisectors unique
Side/Angle Inequalities
*Postulate: Euclid’s 5th
Triangle Angle Sum
Equilat Triangle  60 degree angles
<’s in quad  360
Exterior angle sum theorem
AAS Theorem
2 prs cong corresponding angles  3rd congruent
Only one rt/obtuse angle in triangle
Rt/obtuse angle is biggest in triangle
Side opp rt/obtuse angles is biggest side (hypotenuse is longest)
Rt isos triangles  45, 45, 90
Sum of angles in a n-gon 180(n-2)
Interior angle of a regular polygon: [180(n-2)]/n
Midsegment Theorem
Equilateral quad  llogram
Bisector of ext < of vertex is ll to base iso triangle
Bisectors of opp angles in llogram  cong and ll
Bisectors of corr. <’s of ll lines  ll
Bisectors of s.s int. <’s of ll lines  perp
Rhombus  llogram
Rectangle  llogram
Llogram  opp angles congruent
Llogram  opp sides congruent
Llogram  cons angles supplementary
Llogram  diagonals bisect each other
Midquad of any quadrilateral  llogram
Rectangle  consecutive sides perpendicular
Rectangle  All angles right/90 degrees
Rectangle  congruent diagonals
Llogram with congruent diagonals  rectangle
Llogram with one right angle  rectangle
Rectangle  midquad is rhombus
Rectangle  cyclic
Rhombus  diagonals perpendicular
Llogram with perp diagonals  rhombus
Rhombus  Diagonals bisect opposite angles
Rhombus  miquad is a rectangle
Isos Trap  base angles congruent
Isos Trap  diagonals congruent
Trap with cong base angles  iso trap
Trap with congruent diagonals  iso trap
Iso Trap  midquad rhombus
Iso Trap  cyclic
Iso Trap  cong bowtie triangles, isos hourglass triangles
Kite  1 pr opp cong angles (included angles of non congruent sides)
Kite  perp diagonals
Kite  One diagonal bisects other
Kite  one diagonal bisects angles
Kite  midquad rectangle
Right Kite (II)  cyclic
Comprehensive List of First Semester Definitions
Point
Line
Plane
Line Segment
Ray
Angle
Congruent
Parallel
Intersect
Circle
Polygon
Triangle
Quadrilateral
Perpendicular
Rhombus
Rectangle
Square
Right Angle
Acute Angle
Obtuse Angle
Complimentary Angles
Supplementary Angles
Midpoint
Perpendicular Bisector
Adjacent
Opposite Rays
Linear Pair
Collinear
Angle Bisector
Isosceles Triangle
Equilateral Triangle
Radius
Diameter
Segment Bisector
Altitude
Vertical Angles
Perpendicular Pair
Median
Congruent Triangles
Equivalence Relation
Equilateral
Vertex Angle of an Isosceles Triangle
Base Angles of an Isosceles Triangle
Equiangular
Circumcenter
Incenter
Centroid
Orthocenter
Overlapping Segments/Angles
Exterior Angle
Remote Interior Angle
Transversal
Convex polygon
Concave polygon
Regular Polygon
Midsegment
Trapezoid
Isosceles Trapezoid
Central Angle
Cyclic
Midquad
Diagonal
Kite
Base Angles of trapezoid
Legs of trapezoid
Alternate Interior Angles
Same Side Interior Angles
Corresponding Angles
Concurrent
Between
Logic/System of Mathematics
Postulate
Definition
Theorem
Conjecture
Corollary
Lemma
Counter Example
Biconditional
Conditional
Converse
Inverse
Contrapositive
Logically Equivalent
Inverse Error
Converse Error