Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Segments, Angles and intersections Review Naming 3-D drawing Collinear and Coplanar Intersections Segment Addition Angle Addition Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Review Naming stuff Lines: pick 2 points and draw a line over ‘em A B Segments: draw a segment over the endpoints X Y Z Rays: endpoint first, then any other point. Draw a ray above ‘em R S T Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Basic 3-D Geometry What is the geometric name for the BLUE flat surface? A flat surface is called a plane. Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Basic 3-D Geometry How many planes are pictured here? There are 2 planes the green one and the blue one. Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Basic 3-D Geometry What do the dotted lines mean? They are the “hidden” lines, or the ones you can’t see. Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Basic 3-D Geometry If this object was in your back yard, this is how it would look. Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Basic 3-D Geometry Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Basic 3-D Geometry Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Basic 3-D Geometry Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Collinear & Coplanar Notes Collinear Points on the same line A B C Points A, B and C are collinear Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Collinear & Coplanar Notes Collinear Points on the same line Z Y X Points X, Y and Z are collinear Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Collinear & Coplanar Notes Collinear Points on the same line Points R, S and T Are NOT collinear T S R Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Collinear & Coplanar Notes 2 Points Are always collinear N M Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Collinear & Coplanar Notes Coplanar Points in the same plane Three points are always coplanar Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Basic 3-D Geometry Points A, B and C are coplanar B A C Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Basic 3-D Geometry Points A, B and C are coplanar B C A Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Basic 3-D Geometry Points A, B, C and D are NOT coplanar D B C A Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Review VOCAB Coplanar: on the same plane Q R L T S S,T,L and Q are coplanar R,S,T and Q are NOT coplanar 3 points are always coplanar Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Basic 3-D Geometry A B What is the name for this line? Normally, we would name it with 2 points. Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Basic 3-D Geometry “Intersection” is where two objects “touch” What “shape” do the two planes make where they intersect? A Line. Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Basic 3-D Geometry But this line has no points! So we put its name in the picture Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Review VOCAB Collinear: on the same line T R S R, S and T are collinear L L, M and N are NOT collinear N M 2 points are always collinear Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Review Intersections POINT When lines intersect, they intersect at a ___________. LINE When planes intersect, they intersect at a ___________. Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Naming angles Name a point on one side of the angle. Name the Vertex. Name a point on the other side of the angle. Possible names: A B C Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Supplements First, you have to know what a LINEAR PAIR is Adjacent: Next to. (For angles, it means sharing a side and vertex) These are not adjacent These are adjacent A LINEAR PAIR are adjacent angles that make a straight line. Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Supplements Supplements are any 2 angles whose measures add to 1800 But they do not have to be linear pair 170+10=180 170 10 Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Compliments Compliments are any 2 angles whose measures add to 900 But they do not have to be adjacent 80+10=90 80 10 Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Vertical Angles If we move the Scissors so the red angle gets bigger, What will happen To the yellow angle? Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Vertical Angles If we move the Scissors so the red angle gets bigger, What will happen To the yellow angle? Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Vertical Angles If we move the Scissors so the red angle gets bigger, What will happen To the yellow angle? Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Vertical Angles If we move the Scissors so the red angle gets bigger, What will happen To the yellow angle? Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Vertical Angles EVERY TIME you see this picture… 1. Any angles next to each other add to 180 Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Vertical Angles EVERY TIME you see this picture… 1. Any angles next to each other add to 180 Angles across from each other are equal Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Vertical Angles EVERY TIME you see this picture… 1. Any angles next to each other add to 180 60 Angles across from each other are equal 120 120 60 Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Vertical Angles EVERY TIME you see this picture… 1. Any angles next to each other add to 180 80 Angles across from each other are equal 100 100 80 Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

SAMPLE PROBLEMS 50 110 1. What is the compliment of 400? 2. What is the supplement of 700? 110 Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

SAMPLE PROBLEMS 140 + x = 180 30 + x = 90 X = 60 X = 40 3. Find X Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Vertical Angles Find X, Y and Z 75 X 105 105 Z Y 75 Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Quiz tomorrow: 40 35 8 15 (it will be multiple choice, four questions) BC is the angle bisector. #1 k is the segment bisector. #2 A C x + 20 35 5x 40 B D k 40 35 5X = X + 20 = 8 15 X = X = Friday, February 22, 2019Friday, February 22, 2019 Mr M Kennedy (EDIT)

Segment addition postulate If B is between A and C then AC = AB + BC In other words . . . A C 10 B 20 Then AC = ? 10 + 20 = 30 Friday, February 22, 2019 Mr M Kennedy (EDIT)

Segment addition postulate CONGRUENT Objects that are the same size and shape. (Geometry’s version of equals) D 7 C A 7 B Friday, February 22, 2019 Mr M Kennedy (EDIT)

Segment addition postulate Sample problem: Find XZ X Y Z Friday, February 22, 2019 Mr M Kennedy (EDIT)

ANGLES A B C VERTEX Friday, February 22, 2019 Mr M Kennedy (EDIT)

ANGLES A NAMING Start with a point on one side Then the vertex B Then a point on the other side C Friday, February 22, 2019 Mr M Kennedy (EDIT)

ANGLES TYPES: ACUTE OBTUSE RIGHT STRAIGHT Less than 90 More than 90 90 180 Friday, February 22, 2019 Mr M Kennedy (EDIT)

ANGLES Angle addition postulate: A X B C Friday, February 22, 2019 Mr M Kennedy (EDIT)

ANGLES Sample problem: find A X B C Friday, February 22, 2019 Mr M Kennedy (EDIT)