Basics of Euclidean Geometry

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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.

9. 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

10. 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