Congruence, Similarity and the Triangle Sum Theorem (Part 2) Using Given & Prove
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1 Congruence, Similarity and the Triangle Sum Theorem (Part 2) Using & Prove Up to this point, you have been using proof structure to show your work as you determine all available information on a triangle. Today, you will use true proof structure to determine only what the problem asks you to prove. A proof prompt has two parts:, which is the problem and Prove, which is, essentially, the answer key. Your job is to determine the best way to get from the to the Prove. Keep in mind though, the Prove is the final step and cannot be used anywhere else in your solution. Remember that the Prove statement is the answer, not part of the problem. Symmetric Property of Equality: (Symm. Prop. =) The ability to switch what is on the two sides of the equal sign. 19 = m B m B = 19 Symm. Prop. = : ABC DEF, m A = 58 & m B = 59 Prove: m F = 63 or ABC DEF ABC DEF m A = 58 & m B = 59 m A = 58 & m B = 59 C F m C = 180 m C = m F m C = 180 m C = 63 Subtr. Prop. = m F = 180 C F m F = 180 m C = m F m F = 63 Subtr. Prop. = 63 = m F m F = 63 Symm. Prop. = : ABC DFE, m D = 97 & m E = 26 Prove: m B = 57 or ABC~ DFE ABC~ DFE m D = 97 & m E = 26 m D = 97 & m E = 26 m D + m F + m E = 180 Sum Thm B F 97 + m F + 26 = 180 m B = m F m F = 180 m D + m F + m E = 180 Sum Thm m F = 57 Subtr. Prop. = 97 + m B + 26 = 180 B F m B = 180 m B = m F m B = 57 Subtr. Prop. = m B = 57
2 1. : m B = 89 & m C = 19 Prove: m D = : ABC EDF, m F = 72 & m E = 66 Prove: m B = : ABC FED, m E = 75 & m F = 102 Prove: m C = 3 Congruence, Similarity and the Triangle Sum Theorem Part 2 Page 2
3 4. : m A = 42 & m C = 82 Prove: m E = : ABC FDE, m D = 54 & m F = 89 Prove: m C = : ABC EFD, m E = 64 & m D = 52 Prove: m B = 64 Congruence, Similarity and the Triangle Sum Theorem Part 2 Page 3
4 7. : ABC DFE, m A = 12 & m B = 93 Prove: m E = : ABC EFD, m B = 30 & m C = 90 Prove: m E = 60 Congruence, Similarity & the Triangle Sum Theorem (Part 2) Answers 1. Option A: m B = 89 & m C = 19 m A = 180 m A = 180 m A = 72 Subtr. Prop. = A D m A = m D 72 = m D m D = 72 Symm. Prop. = 2. Option A: ABC EDF, m F = 72 & m E = 66 m E + m D + m F = 180 Sum Thm 66 + m D + 72 = 180 m D = 180 m D = 42 Subtr. Prop. = B D m B = m D m B = Option B: m B = 89 & m C = 19 A D m A = m D m D = 180 m D = 180 m D = 72 Subtr. Prop. = 2. Option B: ABC EDF, m F = 72 & m E = 66 B D m B = m D m E + m D + m F = 180 Sum Thm 66 + m B + 72 = 180 m B = 180 m B = 42 Subtr. Prop. = Congruence, Similarity and the Triangle Sum Theorem Part 2 Page 4
5 , ~ & the Sum Thm (Part 2) Answers Continued 3. Option A: 3. Option B: ABC FED, ABC FED, m E = 75 & m F = 102 m E = 75 & m F = 102 m F + m E + m D = 180 Sum Thm C D m D = 180 m C = m D m D = 180 m F + m E + m C = 180 Sum Thm m D = 3 Subtr. Prop. = m C = 180 C D m C = 180 m C = m D m C = 3 Subtr. Prop. = m C = 3 4. Option A: 4. Option B: m A = 42 & m C = 82 m A = 42 & m C = 82 B E 42 + m B + 82 = 180 m B = m E m B = 180 m A + m E + m C = 180 Sum Thm m B = 56 Subtr. Prop. = 42 + m E + 82 = 180 B E m E = 180 m B = m E m E = 56 Subtr. Prop. = 56 = m E m E = 56 Symm. Prop. = 5. Option A: 5. Option B: ABC FDE, ABC FDE, m D = 54 & m F = 89 m D = 54 & m F = 89 m F + m D + m E = 180 Sum Thm m E = m E = 180 m F + m D + m E = 180 Sum Thm m E = 37 Subtr. Prop. = m C = m C = 180 m C = 37 Subtr. Prop. = m C = Option A: 6. Option B: ABC EFD, ABC EFD, m E = 64 & m D = 52 m E = 64 & m D = 52 m E + m F + m D = 180 Sum Thm B F 64 + m F + 52 = 180 m B = m F m F = 180 m E + m F + m D = 180 Sum Thm m F = 64 Subtr. Prop. = 64 + m B + 52 = 180 B F m B = 180 m B = m F m B = 64 Subtr. Prop. = m B = Option A: 7. Option B: ABC DFE, ABC DFE, m A = 12 & m B = 93 m A = 12 & m B = m C = m C = 180 m C = 75 Subtr. Prop. = m E = m E = 180 m E = 75 Subtr. Prop. = 75 = m E m E = 75 Symm. Prop. = 8. Option A: 8. Option B: ABC EFD, ABC EFD, m B = 30 & m C = 90 m B = 30 & m C = 90 A E m A = 180 m A = m E m A = 180 m A = 60 Subtr. Prop. = m E = 180 A E m E = 180 m A = m E m E = 60 Subtr. Prop. = 60 = m E m E = 60 Symm. Prop. = Congruence, Similarity and the Triangle Sum Theorem Part 2 Page 5
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