Geometry 9/2/14 - Bellwork • 1. Find the measure of MN if N is between M and P, MP = 6x – 2, MN = 4x, and MP = 16. • 2. Name the postulate used to solve the above question.
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Geometry 9/2/14 - Bellwork
• 1. Find the measure of MN if N is between M and P, MP = 6x – 2, MN = 4x, and
MP = 16.
• 2. Name the postulate used to solve the above question.
Bellwork 9/2/14 Answers
2.
1. 12
Geometry 9/3/14 - Bellwork
2.
Bellwork 9/3/14 Answers
1.
2.
2.4 Use Postulates & Diagrams
Objectives:
1. To illustrate and understand postulates about lines and planes
2. To accurately interpret geometric diagrams
6 cm
20 cm
S
M
A
Example 1
What is the length of ?SM
26 cm
S
M
A
You basically used the Segment Addition Postulate to get the length of the segment, where SA + AM = SM.
Example 1
Postulates
- Statements that are never proved but that help in explaining other logical conclusions
Postulates and Theorems
• Postulates are statements in geometry that are so basic, they are assumed to be true without proof.– Sometimes called
axioms.
• Theorems are statements that were once conjectures but have since been proven to be true based on postulates, definitions, properties, or previously proven conjectures.
Both postulates and theorems are ordinarily written in conditional form.
Postulates you need to know…
Through any two points there exists exactly one line.
Postulate 5
Postulate 6
• A line contains at least two points.
If Then
Postulate 7
• If two lines intersect, then their intersection is exactly one point.
If Then
Postulate 8
• Through any three noncollinear points there exists exactly one plane.
If Then
Postulate 9
• A plane contains at least three noncollinear points.
If Then
Postulate 10
• If two points lie in a plane, then the line containing them lies in the plane.
If Then
Postulate 11
• If two planes intersect, then their intersection is a line.
If Then
Example 1
State the postulate illustrated by the diagram.
Answers:
• A) Postulate 7 – when two lines intersect they intersect at a point
• B) Postulate 11- when two planes intersect they intersect at a line
Interpreting Diagrams
When you interpret a diagram, you can assume only information about size or measure if it is marked.
Interpreting Diagrams
Interpreting Diagrams
Perpendicular Figures
A line is perpendicular to a plane if and only if
1) The line intersects the plane in a point and
2) is perpendicular to every line in the plane that intersects it at that point.
Example 4
Which of the following cannot be assumed from the diagram?
1. A, B, and F are collinear.
2. E, B, and D are collinear.
3. AB plane S
Example 4
Which of the following cannot be assumed from the diagram?
4. CD plane T
5. AF intersects BC at point B.
Example 5a
1. Identify all linear pairs of angles.
2. Identify a pair of vertical angles.
4
3
2
1
Answer: 1) <1 and <2, <2 and <3, <3 and <4,
<1 and <42) <2 and <4
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
Do we have to prove this?
Vertical Angle Congruence Theorem
Vertical angles are congruent.
Geometry Homework Due 9/4/14
• Textbook pp. 99 – 102• Exercises: 1 – 24 All
46 – 56 All
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