1.

Identify the correct justification for each step, given that AC intersects BE, m/AFE = 40* and m/CFD =50%. C E F B A It is given that AC intersects BE. By the LAFE and ZBFC are vertical _ s. By the LAFE ~ ZBFC. By the m/AFE=m/BFC. It is given that m/AFE = 40* . So, m/BFC = 40 by the By the m/BFD =m/BFC +m/CFD. It is given that m/CFD = 50. So, m/BFD = 40* + 50* by the Simplify to get m/BFD = 90". Thus, /BFD is a right _ byIt is given that AC intersects BE. By the definition of vertical /s, ZAFE and /BFC are vertical /s. By the Vertical /s Thm., LAFE ~ /BFC. By the definition of vert /s, m/AFE=m/BFC. It is given that m/AFE = 40. So, m/BFC = 40" by the Subst. Property of =. By the / Addition Post., m/BFD =m/BFC + m/CFD. It is given that m/CFD =50. So, m/BFD = 40' + 50* by the Subst. Property of =. Simplify to get m/BFD =90. Thus, /BFD is a right _ by the definition of comp. /s. O It is given that AC intersects BE. By the definition of vertical /s, LAFE and /BFC are vertical /s. By the Vertical /s Thm., LAFE ~ /BFC. By the definition of ~ Zs, m/AFE=m/BFC. It is given that m/AFE = 40". So, m/BFC = 40' by the Subst. Property of =. By the _ Addition Post., m/BFD =m/BFC+m/CFD. It is given that m/CFD =50. So, m/BFD = 40* +50" by the Subst. Property of =. Simplify to get m/BFD =90. Thus, /BFD is a right _ by the definition of right s.It is given that AC intersects BE. By the definition of vertical /s, ZAFE and ZBFC are vertical /s. By the definition of ~ , LAFE ~ /BFC. By the definition of ~ Zs, myAFE = m/BFC. It is given that m/AFE = 40 . So, m/BFC = 40' by the Trans. Property of ~ . By the defintion of supp. Zs, m/BFD =m/BFC +m/CFD. It is given that m/CFD = 50'. So, m/BFD = 40* +50 by the Add. Property of =. Simplify to get m/BFD =90. Thus, ZBFD is a right _ by the definition of right _s. O It is given that AC intersects BE. By the definition of vertical /s, ZAFE and Z BFC are vertical /s. By the definition of ~ , ZAFE ~ /BFC. By the definition of ~ Zs, m/AFE=m/BFC. It is given that m/AFE = 40'. So, m/BFC = 40' by the Subst. Property of =. By the defintion of supp. Zs, m/BFD =m/BFC+ m/CFD. It is given that m/CFD =50*. So, m/BFD = 40* + 50* by the Subst. Property of =. Simplify to get m/BFD =90. Thus, ZBFD is a right _ by the definition of comp. _s.Identify the correct justification for each step, given that m/1 = 40" and m/2 = 40". E D 2 2 4 1. m/1 = 40', m/2 =40' 2. m/1+m/3=m/ABD 3. Z2 and ZABD are supplementary 4. m/2+ m/ABD = 180* 5. m/2+ m/1 + m/3 = 180 6. 40' + 40* + m/3 =180" 7. 80" + m/3 = 180* 8. m/3 = 100*O 1. Given 2. 2 Add. Post. 3. Lin. Pair Thm. 4. Def. of Supp. 25 5. Subst. Prop. of = 6. Subst. Prop. of = 7. Simplify 8. Subt. Prop. of = O 1. Given 2. 2 Add. Post. 3. Vert. 2 5 Thm. 4. Def. of Supp. 25 5. Subst. Prop. of = 6. Add. Prop. of = 7. Simplify 8. Mult. Prop. of = O 1. Given 2. z Add. Post. 3. Vert z s Thm. 4. Def. of Comp. 25 5. Add. Prop. of = 6. Add. Prop. of = 7. Simplify 8. Mult. Prop. of = O 1. Given 2. z Sub. Post. 3. Lin. Pair Thm. 4. Def. of Comp. 25 5. Add. Prop. of = 6. Subst. Prop. of = 7. Simplify 8. Subt. Prop. of =Determine whether the statement is true or false. If false, give a counterexample. If t2 = 289, then t = -17. O false; t = 17 O false; t = 13 O false; t = 19 trueIdentityr the converse and a hiconditional statement for the conditional. If an angle is acute: then its measure is less than 90". C} converse: If an angle measures greater than ED", then the angle is obtuse. biconditional: An angle is acute if and only if its measure is less than 311. converse: If an angle measures greater than 91]", then the angle is acute. biconditional: An angle is obtuse if and only.r if its measure is less than Ell\". converse: If an angle measures less than 911'\Determine if this conjecture is true. If not, give a counterexample. The sum of two negative numbers is less than -1. O false; 0 + (-1) = -1 true O false; -1 + (-1) -1