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Proving the Congruent Supplements Theorem
Try
Statements Reasons
Given: 21 and 22 are supplements, 23
and 24 are supplements, and
2124
Prove. 22 23
m2 1 + m 2 = 180
m23+ m24 = 180
21 and 22 are supp.
23 and 24 are supp
21 24
m2 1 + m 2 = m 3 + m24
Statements
Reasons
3
2
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Proving the Congruent Supplements Theorem Try Statements Reasons Given 21 and 22 are supplements 23 and 24 are supplements and 2124 Prove 22 23 m2 1 m 2 180 m23 class=

Respuesta :

Answer:

From

m∠1 = m∠4  

m∠1 + m∠2 = m∠3 + m∠4

m∠2 = m∠3 [tex]{}[/tex]                                                Identity property

∠2 ≅ ∠3 [tex]{}[/tex]                                      [tex]{}[/tex]               Equal angles are congruent

Step-by-step explanation:

Given [tex]{}[/tex]                                                                            Reason

∠1 and ∠2 are supplementary    [tex]{}[/tex]             Given

Therefore;

m∠1 + m∠2 = 180°                              [tex]{}[/tex]       Supplementary ∠s sum up to 180°

∠3 and ∠4 are supplementary    [tex]{}[/tex]             Given

Therefore;

m∠3 + m∠4 = 180°                              [tex]{}[/tex]       Supplementary ∠s sum up to 180°

From which we have;

m∠1 + m∠2 = 180° = m∠3 + m∠4       [tex]{}[/tex]   [tex]{}[/tex]    Transitive property

m∠1 + m∠2 = m∠3 + m∠4

∠1 ≅ ∠4                          [tex]{}[/tex]                             Given

m∠1 = m∠4                                    [tex]{}[/tex]              Congruent ∠s have equal measure

Therefore;

m∠1 + m∠2 = m∠3 + m∠1              [tex]{}[/tex]         [tex]{}[/tex]   Transitive property

Therefore;

m∠1 + m∠2 - m∠1= m∠3 + m∠1 - m∠1       [tex]{}[/tex]Subtraction property

m∠1 - m∠1 + m∠2 = m∠3 + m∠1 - m∠1  [tex]{}[/tex]    

0 + m∠2 = m∠3 + 0                             [tex]{}[/tex]       Inverse property

Therefore;

m∠2 = m∠3 [tex]{}[/tex]                                                Identity property

∠2 ≅ ∠3 [tex]{}[/tex]                                      [tex]{}[/tex]               Equal angles are congruent.

jadyen

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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