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Geo CP Day 23 > SWBAT state the midpoint and angle bisector theorem.

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Geo CP Day 23 > SWBAT state the midpoint and angle bisector theorem.

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  1. What does it mean to respect the sacrifice our forefathers and mothers have made for us. It means to dance on their graves. It means to remember that every square foot of our country is hallowed ground, bought with their blood. That every tree, every blade of grass, every moment is a monument to the price they paid for our freedom. To bring any less than our best to this sacred reality of our days is to disrespect rather than dance on their graves. --Anon

  2. Geo CP Day 23 >SWBAT state the midpoint and angle bisector theorem. >SWBAT use these theorems in proofs. > SWBAT show perfection in doing basic proofs not involving midpoint and angle bisector theorems. Pg. 46: 1,2,5,6, 9, 13, 15, 17, pg. 42: 13

  3. A M B Segment Addition p1 + p2 = w • M Btwn A,B  AM + MB = AB • M Midpt A,B  AM = MB • M Midpt. A,B  ½ AB = AM or MB Def. of Midpoint p1 = p2 Segment Postulates and Theorems Midpoint Theorem ½ W = p1 or p2

  4. A 1 M X 2 B Angle Addition p1 + p2 = W • XM Btwn XA, XB  m<1 + m<2 = m<AXB • XM Bisects <AXB  m<1 = m<2 • XM Bisects <AXB  ½ m<AXB = m<1 Angle Postulates and Theorems Def. of < Bisector p1 = p2 < Bisector Theorem ½ W = p1

  5. M B A 1 2 X Def. of a Straight Angle m<1 + m<2 = 180 m<AXM + m<MXB = 180

  6. Addition Prop of = Subtraction Prop of = Multiplication Prop of = Division Prop of =

  7. Reflexive Prop of = Symmetric Prop of = Properties of Equality a = a If a = b, then b = a If a = b and b = c then a = c Transitive Prop of =

  8. Given • m<1 = m<2 • m<3 = m<4 2. m<1 + m<3 = m<2 + m<4 Add prop = Given: m<1 = m<2; m<3 = m<4 #11 Prove: m<SRT = m<STR 3. m<1 + m<3 = m<SRT m<2 + m<4 = m<STR Angle add post 4. m<SRT = m<STR Subtit prop =

  9. Given • m<SRT = m<STR 2. m<SRT = M<3 + m<1 m<SRT = M<4 + m<2 Angle Add Post 3. m<3 + m<1 = m<4 + m<2 Substitution Given: m<SRT = m<STR; m<3 = m<4 #14 Prove: m<1 = m<2 4. m<3 = m<4 Given 5. m<1 = m<2 Subtr prop =

  10. 1. DW = ON 1. Given 2. DW = DO + OW ON = ____ + ____ Given: DW = ON #9 Prove: DO = WN 3. ______ 3. Substitution 4. OW = OW 4. ___________ 5. _____________ 5. ___________

  11. 1. RP = TQ 1. Given PS = QS 2. RP + PS = TQ + QS 2. Add. Prop = Given: RP = TQ & PS = QS #12 Prove: RS = QS 3. RP + PS = RS 3. Seg. Add. = 4. RS = TQ + QS 4. Substitution 5. _____________ 5. ___________

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