DO NOW Identify whether these statements below can

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. ” 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 1

PAGE 99 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. 20) No; a = 2, b = – 2 21) Yes 22) No; y = – 8 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 23) No; x = – 2 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 10) 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 2

ASSUMPTIONS, JUSTIFICATIONS, AND CONCLUSIONS Geometry Pre. AP, Revised © 2013 viet. dang@humble. k 12.

DEFINITIONS A. Assumptions are “a thing that is accepted as true or as certain to happen, without proof” B. Justifications are “something (such as a fact or circumstance) that shows an action to be reasonable or necessary” 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 4

WHAT CAN YOU ASSUME FROM THIS PICTURE? 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 5

WHAT CAN YOU ASSUME FROM THIS PICTURE? 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 6

EXAMPLE 1 List the facts you can assume from it. Intersect at point H Points are collinear 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 7

ASSUMPTIONS Definition: YOU & ME 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 8

JUSTIFICATIONS Without any doubt 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 9

EXAMPLE 2 Given the image, determine “m AEB is acute” is a true or false statement. FALSE 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 10

EXAMPLE 3 FALSE 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 11

YOUR TURN 12/23/2021 5: 23 PM FALSE, TRUE Assumptions, Justifications, and Conclusions 12

EXAMPLE 4 Law of Congruent 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 13

EXAMPLE 5 Law of Midpoint 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 14

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 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 15

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 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 16

EXAMPLE 7 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 17

EXAMPLE 8 Use the information to establish the conclusion and justification, Given: CO = OL 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 18

EXAMPLE 9 Use the information to establish the conclusion and justification, Given the diagram below. K M 7 5 E I 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 19

YOUR TURN Use the information to establish the conclusion and justification, Given: A is between J and M. 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 20

ASSIGNMENT Worksheet 12/23/2021 5: 23 PM Assumptions, Justifications, and Conclusions 21