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

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

Assumptions, Justifications, and Conclusions Geometry PreAP, Revised ©2013 viet.dang@humble.k12.tx.us 11/12/2018 3:33 PM Assumptions, Justifications, and Conclusions

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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