Basics of Euclidean Geometry Point Line Number line Segment Ray Plane Coordinate plane One letter names a point Two letters names a line, segment, or ray (or small script) Three letters names a plane (or capital script) Collinear vs. Coplanar Segment addition Midpoint formula (find the avg of (x,y)) = (x1+x2)/2, (y1+y2)/2 Absolute value

Basics of Euclidean Geometry Numerical Patterns Conjecture Counter- examples Types of patterns – arithmetic, geometric, quadratic, other Describe patterns in words or by formulas Write a conjecture Use a counterexample to show a conjecture is false

Basics of Euclidean Geometry Intersections Segment measurement Angles Angle measurement Table of intersections Using a ruler or number line to find length Naming an angle One letter = vertex Number = opening Three letters = connection of rays Types of angles Acute, Obtuse, Right, Straight Measures in Degrees

Angles and Angle relationships Angle pairs Adjacent Linear Vertical Complementary Supplementary Congruence marks Angles that share a side and vertex Angles that share a side, vertex, and make a line Linear pairs are supplementary Angles that are opposite and share a vertex All vertical angles are congruent Two angles whose sum is 90 degrees Two angles whose sum is 180 degrees

Properties of Equality and Congruence Reflexive Symmetry Transitive Addition Subtraction Multiplication Division Distributive A = A X+3 = 7 so 7 = X+3 If a=b and b=c then a=c If x=5 then x+4= 5+4 If x=5 then x-3= 5-3 If x=5 then 6x= 5*6 If x=5 then x / 2 = 5 / 2 If 3(x+5) then 3x + 15

Intersections and Linear Relationships Intersecting Lines Perpendicular Non- intersecting Lines Skew Parallel Two lines that intersect form pairs of vertical and linear pairs of angles Two lines are perpendicular if they form a right angle “Duh” theorems Two lines intersected by a third line (transversal) form: Corresponding angles Alternate Interior Alternate Exterior Same Side Interior Same Side Exterior

Intersections and Linear Relationships Parallel Lines Congruent angle pairs Supplementary angle pairs How to prove that two lines are parallel Using slope to show 2 lines are parallel or perpendicular Two lines in the same plane, equidistant from each other that do not intersect are Parallel Two parallel lines intersected by a transversal form congruent: Corresponding angles Alternate Interior Alternate Exterior Two parallel lines intersected by a transversal form supplementary: Same Side Interior Same Side Exterior Parallel lines have equal slopes Perpendicular lines have opposite, reciprocal slopes

Logical Statements Statements that have true or false value Conditional Converse Inverse Contrapositive Should not include opinions; only observational that must have a definite outcome If it is sunny, then the shades are down. If the shades are down, then it is sunny. If it is not sunny, then the shades are not down. If the shades are not down, then it is not sunny.

Triangles Definition and Name Types Basic properties and Theorems A flat (plane), three sided (three segments), closed (joined at their endpoints) figure Name three points in any order Types by side : Scalene, Isosceles, Equilateral Types by angle : Acute, Obtuse, Right, Equiangular Triangle Inequality Angle Sum Theorem Exterior Angle Theorem

Triangles Congruence 5 shortcuts to prove triangles are congruent SSS SAS ASA AAS HL Identifying corresponding congruent parts Name missing or corresponding parts Side – Side – Side Side – Angle – Side Angle – Side – Angle Angle – Angle – Side Hypotenuse - Leg