Common Core State Standards GMG3 Apply geometric methods to solve problems Student Learning Targets 1 Students will be able to identify and use basic postulates about points lines and planes ID: 733124
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2.5 Notes: Postulates and Paragraph Proofs
Common Core State Standards
G.MG.3 Apply geometric methods to solve problems.
Student Learning Targets
1. Students will be able to identify and use basic postulates about points, lines and planes.
2. Students will be able write paragraph proofs. Slide2
VOCAB
Vocabulary
Definition
Real Life Example Postulate
A statement accepted as true without proof. Slide3
VOCAB
Points, Lines, and Planes Postulates
Postulate
DefinitionPicture 2.1
2.2 2.3
Exactly one line through any two points.
One plane through any three non-collinear points.
One line contains
at least
two points. Slide4
VOCAB
2.4
2.5
One plane contains at least three non-collinear points. If two points are on a plane, the line containing the points are also in the plane. Slide5
Intersection of Lines and Planes
Postulate
DefinitionPicture 2.6
2.7
Two lines intersect at exactly one point. Two planes intersect at one line. Slide6
Example 1:
Explain how the picture illustrates that the statement is true. Then state the postulate that can be used to show the statement is true.
a) Lines n and l intersect at point K. b)Planes P and Q intersect in line m. c) Points D, K, and H determine a plane. d) Point D is also on the line n through points C and K. e) Points D and H are collinear. f) Points E, F and G are coplanar. Slide7
Example 2:
You can use postulates to explain your reasoning when analyzing statements.
Determine
whether the following statement is always, sometimes, or never true. Explain. If plane T contains and contains point G, then plane T contains point G.b) contains three non-collinear points.
Slide8
VOCAB
Vocabulary
Definition
Real Life Example Proof
Theorem
A logical argument in which each statement made can be accepted as true. When a statement or conjecture has been proven. Slide9
The Proof Process
Step 1:
Step 2: Step 3:
Step 4:
Step 5: List the given information and draw a diagram if possible. State what needs to be proven. Create an argument by forming a chain of statements that link the given information to what you are trying to prove. Use definitions, algebraic properties, postulates, and theorems to support your statements listed in step 3. State what you just proved. Slide10
Brain Break
Who won
Superbowl
1?What has no beginning, end, or middle?Slide11
Example 3:
Use
the steps above to prove the given statement.
Given intersects , write a paragraph proof to show that A, C, and D determine a plane. Slide12
VOCAB
Vocabulary
Definition
Picture Midpoint Theorem
If M is the midpoint of
, then
Slide13
Summary
Explain how the figure illustrates that each statement is true. Then state the postulate that can be used to show each statement is true.
1. Planes P and Q intersect in line r. 2. Lines r and n intersect at point D. 3. Lines n contains points C, D, and E. 4. Plane P contains the points A, F, and D. 5. Line n lies in plane Q. 6. line r is the only line through points A and D. Slide14
Summary
Determine
whether each statement is
always, sometimes or never true. Explain your reasoning. 7. The intersection of three planes is a line. 8. Line r contains only point P. 9. Through two points, there is exactly one line.