2­5 Postulates and Paragaph Proofs.notebook
October 06, 2015
10­6 Honors Geometry Warm­up: Fill in the blanks in your packet.
2­5 Postulates and Paragraph Proofs Postulate: a statement that describes a fundamental relationship between basic terms of geometry
2.1 Through any two points, there is exactly _____ line.
2.2 Through any three points not on the same line, there is exactly ____ plane.
2.3 A line contains at least____ points.
2.4 A plane contains at least _____ points not on the same line.
2.5 If two points lie in a plane, then the entire line containing those points lies in that plane.
2.6 If two lines intersect, then their intersection is exactly ­­­­­____ point.
2.7 If two planes intersect, then their intersection is a __________.
Theorem: a statement or conjecture shown to be __________.
Proof: a logical argument in which each statement you make is supported by a statement that is accepted as true.
*The textbook often tells you to write a paragraph proof. We will instead write a ...
Two­column proof: a formal proof that contains _________________ and _________________ organized in two columns. Each step is called a __________________ and the properties that justify each step are called ________________________.
Steps to a good proof
1. List the ______________ information.
2. Draw a diagram to illustrate the given information (if possible).
3. Use __________________ reasoning.
4. State what is to be _____________.
2­5 Postulates and Paragaph Proofs.notebook
October 06, 2015
Definition of Congruent Segments: Definition of Congruent Angles: Midpoint Theorem: If M is the midpoint of AB, then
Statement
Reason
Paragraph proof of the Midpoint Theorem: From the definition of midpoint of a segment, AM = MB. (This means that AM and MB have the same measure.) By the definition of congruent segments, if two segments have the same measure then they are congruent. Thus
. 2­5 Postulates and Paragaph Proofs.notebook
October 06, 2015
2­5 Postulates and Paragaph Proofs.notebook
October 06, 2015
28
21
Always, (2.7 and 2.3 combo)
Sometimes, 3 planes can just have 1 point in common.
2.5
2.6
Statement
Reason Given
AE = EB and CE = ED
Def. of mipt
need to learn the segment addition postulate to complete the rest of the proof.
The two intersecting planses are the plane that contains A, B, and C and the plane that contains B, C, and D.
Attachments
Chapter 1 Test.docx