1. Assumptions, Justifications, and Conclusions
Do NOW
Identify whether these statements below can be made into biconditional statements. If it cannot, provide a counterexample. 1) “If a polygon has five sides, then it is a regular pentagon.” 2) “If the sum of two angles equals 180°, then the angles are supplementary.” 3) “Supplementary angles are always linear pairs.”
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

2. Assumptions, Justifications, and Conclusions
Page 99
10)
Conditional: If three points are coplanar, then they lie on the same plane.
Converse: If three points lie on the same plane, then they are coplanar.
13)
Conditional: If it is the weekend, then today is Saturday or Sunday.
Biconditional: Today is Sat or Sun if and only if it is the weekend
16)
False: Felipe could play other sports
17)
True
18)
It is a circle iff it is the set of all points that are fixed distance from a given point
19)
The player is a catcher iff the player is positioned behind home plate and catches throws from pitcher
20)
No; a = 2, b = –2
21)
Yes
22)
No; y = –8
23)
No; x = –2
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

3. Assumptions, Justifications, and Conclusions
Geometry PreAP, Revised ©2013
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

4. Assumptions, Justifications, and Conclusions
Definitions
Assumptions are “a thing that is accepted as true or as certain to happen, without proof”
Justifications are “something (such as a fact or circumstance) that shows an action to be reasonable or necessary”
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

5. What Can You Assume From This Picture?
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

6. What Can You Assume From This Picture?
Points A, B, and C are collinear
mABD is obtuse
𝐴𝐵 ≅ 𝐶𝐷
𝐴𝐶 is a line
ABD and CBD are adjacent angles
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

7. Assumptions, Justifications, and Conclusions
Example 1
List the facts you can assume from it.
Intersect at point H
Points are collinear
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

8. Assumptions, Justifications, and Conclusions
Definition:
YOU & ME
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

9. Assumptions, Justifications, and Conclusions
Without any doubt
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

10. Assumptions, Justifications, and Conclusions
Example 2
Given the image, determine “mAEB is acute” is a true or false statement.
FALSE
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

11. Assumptions, Justifications, and Conclusions
Example 3
Given the image, determine “ 𝑬𝑻 ∥ 𝑺𝑹 ” is true or false.
FALSE
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

12. Assumptions, Justifications, and Conclusions
Your Turn
Given the image, determine “mBEC and mECB are supplementary,” “C is the midpoint of 𝑩𝑫 ” and “ABE and EBC” is a true or false statement.
FALSE, FALSE, TRUE
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

13. Assumptions, Justifications, and Conclusions
Example 4
For each statement and its next logical conclusion, tell which definition, postulate, or theorem gives the justification. Given: 𝑨𝑴 ≅ 𝑾𝑼 Conclusion: AM = WU
Law of Congruent
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

14. Assumptions, Justifications, and Conclusions
Example 5
For each statement and its next logical conclusion, tell which definition, postulate, or theorem gives the justification. Given: E is the midpoint of 𝑩𝑫 Conclusion 𝑩𝑬 ≅ 𝑬𝑫
Law of Midpoint
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

15. Assumptions, Justifications, and Conclusions
Example 6
For each statement and its next logical conclusion, tell which definition, postulate, or theorem gives the justification. Given: A is in the interior of mGLD Conclusion mGLA + mALD = mGLD
Definition of Angle Addition Postulate
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

16. Assumptions, Justifications, and Conclusions
Your Turn
For each statement and its next logical conclusion, tell which definition, postulate, or theorem gives the justification. Given: DAY and YAK are a linear pair Conclusion DAY and YAK are supplementary
Definition of Linear Pair Theorem
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

17. Assumptions, Justifications, and Conclusions
Example 7
Use the information to establish the conclusion and justification, Given: 𝑻𝑶 ≅ 𝑨𝑵
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

18. Assumptions, Justifications, and Conclusions
Example 8
Use the information to establish the conclusion and justification, Given: CO = OL
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

19. Assumptions, Justifications, and Conclusions
Example 9
Use the information to establish the conclusion and justification, Given the diagram below. E K I M 5 7
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

20. Assumptions, Justifications, and Conclusions
Your Turn
Use the information to establish the conclusion and justification, Given: A is between J and M.
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions

21. Assumptions, Justifications, and Conclusions
Assignment
Worksheet
11/12/2018 3:33 PM
Assumptions, Justifications, and Conclusions