Download Geometry Fall 2016 Lesson 017 _Using postulates and theorems to

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Lesson Plan #17
Date: Friday October 21st, 2016
Class: Geometry
Topic: Using postulates and definitions to prove statements in geometry
Aim: Students will be able to use postulates and definitions to prove statements in geometry?
HW #17:
Prove the conclusions in 7
Objectives:
Students will be able to use definitions, postulates and theorems to prove statements.
Note:
Below are the theorems we proved yesterday
 Theorem - If two angles are right angles, then they are congruent
 Theorem - If two angles are straight angles, then they are congruent
 Theorem - If two angles are complements of the same angle, then they are congruent
 Theorem - If two angles are supplements of the same angle, then they are congruent
 Theorem – If two angles are congruent, their complements are congruent.
 Theorem – If two angles are congruent their supplements are congruent
Do Now:
Recall the definition of a linear pair:
A linear pair of angles are two adjacent angles whose sum is a straight angle.
Fill in the missing reason in the proof
Given:
<1 and <2 form a linear pair
Prove:
 1 is supplementary to angle  2
Statements
1.  1 and  2 form a linear pair
2.  1  2 is a straight angle.
3. m  1  m  2  180
4. <1 is supplementary to angle <2
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
What theorem was just proven in the Do Now?
Theorem: If two angles form a linear pair, they are supplementary
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Reasons
1. Given
2. Definition of a linear pair
3.
4. Definition of supplementary angles
1
2
Assignment #2: Fill in the missing reason in the proof
B
Given:
C
 BEC and  AED are vertical angles
E
Prove:
D
 BEC  AED
A
Statements
Reasons
1. Given
2. Definition vertical angles. (1)
 BEC and  AED are vertical angles
2. AEC and CED intersect at E.
3. AEC & BEC form a linear pair of angles.
AED & AEC form a linear pair of angles
1.
3. Definition of a linear pair of angles (2)
3. <BEC is the supplement of <AEC.
<AED is the supplement of <AEC.
4. <BEC  <AED

3.
4.
Theorem – If two angles are vertical angles, then they are congruent.
Assignment #3:
Complete the proof at the right.
ect
Assignment #4: Fill in the missing reasons
Statements
Reasons
1. CE bisects  ADB
1.
2.  ADE  BDE
2.
3. FDB and
3.
CDE intersect.
4.  BDE and  FDC are
vertical angles
5.  BDE  FDC
4.
6.
6. Transitive Property of congruence (2,5)
5.
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Assignment #5: Prove the following statement.
Statements
1.
Reasons
1.
Sample Proof:
Statements
1. ABC
2.  r  s
3. m  r  m  s
4. BE bisects  CBD
5. BF bisects  CBG
6. m  CBE  m  x  m  r  180
7. m  CBF  m  y  m  s  180
8. m  CBE  m  x  m  r  m  CBF  m  y  m  s
9. m  r  m  s
10. m  CBE  m  x  m  s  m  CBF  m  y  m  s
11. m  s  m  s
12. m  CBE  m  x  m  CBF  m  y
13.  CBE   x
14. m  CBE  m  x
15.  CBF  y
16. m  CBF  m  y
17. m  x  m  x  m  y  m  y
2m  x  2m  y
or
18. m  x  m  y
19.  x  y
Reasons
1. Given
2. Given
3. Definition of congruent angles (2)
4. Given
5. Given
6. Postulate – The sum of the degree measures
of all the angles on one side of a given line
whose common vertex is a given point on the
line is 180 (1)
7. Same as reason 6 (1)
8. Transitive Property of Equality (6, 7)
9. Definition of congruent angles (2)
10. Substitution Postulate (8,9)
11. Reflexive Property of Equality
12. Subtraction Postulate (10,11)
13. Definition of an angle bisector (4)
14. Definition of congruent angles (13)
15. Definition of an angle bisector (5)
16. Definition of congruent angles
17. Substitution Postulate (12, 14, 16)
18. Division Postulate (17)
19. Definition of congruent angles (18)
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Chapter Review:
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Assignment #6: