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lukranit [14]
3 years ago
8

Proving the Congruent Supplements Theorem

Mathematics
2 answers:
lianna [129]3 years ago
5 0

Answer:

From

m∠1 = m∠4  

m∠1 + m∠2 = m∠3 + m∠4

m∠2 = m∠3 {}                                                Identity property

∠2 ≅ ∠3 {}                                      {}               Equal angles are congruent

Step-by-step explanation:

Given {}                                                                            Reason

∠1 and ∠2 are supplementary    {}             Given

Therefore;

m∠1 + m∠2 = 180°                              {}       Supplementary ∠s sum up to 180°

∠3 and ∠4 are supplementary    {}             Given

Therefore;

m∠3 + m∠4 = 180°                              {}       Supplementary ∠s sum up to 180°

From which we have;

m∠1 + m∠2 = 180° = m∠3 + m∠4       {}   {}    Transitive property

m∠1 + m∠2 = m∠3 + m∠4

∠1 ≅ ∠4                          {}                             Given

m∠1 = m∠4                                    {}              Congruent ∠s have equal measure

Therefore;

m∠1 + m∠2 = m∠3 + m∠1              {}         {}   Transitive property

Therefore;

m∠1 + m∠2 - m∠1= m∠3 + m∠1 - m∠1       {}Subtraction property

m∠1 - m∠1 + m∠2 = m∠3 + m∠1 - m∠1  {}    

0 + m∠2 = m∠3 + 0                             {}       Inverse property

Therefore;

m∠2 = m∠3 {}                                                Identity property

∠2 ≅ ∠3 {}                                      {}               Equal angles are congruent.

denis23 [38]3 years ago
4 0

Answer:

  1. <1 and <2 are supp. given
  2. m <1+ m<2 =180. def. of supplementary angles
  3. <1≅<4. given
  4. <3 and <4 are supp. given
  5. m< 3 + m<4 = 180. def. of supplementary angles
  6. m<1+m<2 = m< 3 + m<4. substitution property
  7. m<1 = m<4. definition of ≅ angles
  8. m<1+m<2 = m< 3 + m<1. Substitution property
  9. m<2 = m< 3. subtraction property
  10. <2 ≅ < 3. definition of ≅ angle

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