Lesson 1.1 Building Blocks of Geometry Good Morning Lesson 1.1 Building Blocks of Geometry Homework: Geometry - Lesson 1.1/ 1-31 odds Quiz Friday – Lesson 1.1

Basic Geometric Figures Undefined terms: Line Point Plane

.A Point Points have NO size and are often shown as dots. HOW TO WRITE: ♥ Points are named as ONE capital letter such as A or X .A

Lines A line has no thickness, but has infinite length. It is an straight arrangement of an infinite amount of points. HOW TO WRITE: ♥ Lines are named by two points (capital letters) on the line, topped with miniature version of a line on top. Or ♥ a single lowercase script letter. X. Y.     m line m

Plane A plane has length and width, but no height. It extends infinitely in all directions along a flat surface. HOW TO WRITE: ♥ A plane can be named by three points (THREE capital letters) that lie in the plane. Or ♥ It can be named by one script capital letter such as R. A. C. B. Plane ABC Plane R R

Collinear Coplanar X. Z. Y. Points on the same line, together. Points X, Y, & Z are collinear Coplanar Points, lines, …, on the same plane, together A. C.   B.

Segment A segment is a part of a line that begins at one point and ends at another. The points are called the endpoints of the segment. HOW TO WRITE: The endpoints are capital letters and have a bar over them. G H  

Ray A ray is a part of a line that starts at a point and goes infinitely in one direction. The point is called the endpoint of the ray HOW TO WRITE: Two capital letters with a ray on top. Be sure to have the endpoint above the endpoint letter! Q P P Q  

Angle An angle is formed by two rays with a common endpoint. The endpoint is called the vertex of the angle and the rays are the sides of the angle. An angle divides a plane into two regions: the interior and the exterior.

Angles HOW TO NAME IT: Use THREE capital letters with the vertex in the middle and the angle sign in front. The three letters need to be in the order that they would be if you traced the angle with your finger. OR By the angle sign and the vertex ONLY IF there is only one angle at the vertex.   D F   E  

Multiple angles with a shared vertex   C B     D   E There are 4 angles with vertex B, therefore each angle MUST be named using 3 points specific to that angle.

CONGRUENT  CONGRUENT means the same size and same shape CONGRUENT LINE SEGMENTS means two line segments are the same size Show congruent segments by making identical markings on each. Parts with the same amount of markings are congruent Slash or tick marks E R ● ● I ● Q ● M A H T

Congruent vs. Equal -Recall the difference between the following - we can manipulate an equation by adding, multiplying etc. - we cannot do much with a congruency statement other than reflexive, symmetric, transitive - so when we have a congruency statement and want to manipulate it my adding, subtracting, etc. we must change it to an equation statement.   -refers to the physical geometric objects (segments) that are the same size and shape.   -refers to two numbers (the measures of the segments) that are equal.

What's the story on this notation between things that are congruent and those that are equal? The notation used in geometry can often be confusing.  The major problems seem to develop when working with segments and angles.  Let's see if we can clarify "what" gets used "when".   Basic knowledge:  with the bar on top, means the actual segment itself.   without the bar on top, means the length of the segment labeled A and B. means the actual angle itself.   means the measure of the angle labeled A, B and C.  

Midpoint Midpoint of a segment is the point on the segment that is the same distance from both endpoints bisects the segment divides the segment into two congruent segments Congruent markings on a segment indicate a point is a midpoint E U Q ● ● ● Congruent markings, aka, slash marks

Midpoint of WHAT? Can a point have a midpoint ? a line? a square? a plane? NO, only a segment is finite in length There is NO midpoint to infinity

Conjectures A conjecture is a statement that is accepted as true without proof. In other words, a conjecture is so obvious, and makes so much sense, there is no need to prove it.

Our first 5 Conjectures The intersection of two lines is a ________ The intersection of two planes is a ______. Through any two points there is exactly one _______. Through any three noncollinear points there is exactly one ______. If two points are in a plane, then the line containing them ____________________. POINT LINE LINE PLANE IS ALSO IN THE PLANE.