Basics of Euclidean Geometry Point Line Number line Segment Ray Plane Coordinate plane One letter...
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![Page 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.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649f135503460f94c2778d/html5/thumbnails/1.jpg)
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
![Page 2: 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.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649f135503460f94c2778d/html5/thumbnails/2.jpg)
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
![Page 3: 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.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649f135503460f94c2778d/html5/thumbnails/3.jpg)
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
![Page 4: 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.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649f135503460f94c2778d/html5/thumbnails/4.jpg)
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
![Page 5: 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.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649f135503460f94c2778d/html5/thumbnails/5.jpg)
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
![Page 6: 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.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649f135503460f94c2778d/html5/thumbnails/6.jpg)
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
![Page 7: 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.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649f135503460f94c2778d/html5/thumbnails/7.jpg)
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
![Page 8: 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.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649f135503460f94c2778d/html5/thumbnails/8.jpg)
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.
![Page 9: 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.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649f135503460f94c2778d/html5/thumbnails/9.jpg)
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
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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
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