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Complete the following paragraph proof:

Given: ∠5 and ∠7 are supplementary. ∠7 and ∠9 are also supplementary.
Prove: ∠5 ≅ ∠9

We know that ∠5 and ∠7 are supplementary. ∠7 and ∠9 are also supplementary because [tex]\( m∠5 + m∠7 = 180^\circ \)[/tex] and [tex]\( m∠7 + m∠9 = 180^\circ \)[/tex] by the definition of supplementary angles. Then, [tex]\( m∠5 + m∠7 = m∠7 + m∠9 \)[/tex] by the Transitive Property. Subtract [tex]\( m∠7 \)[/tex] from each side and you get [tex]\( m∠5 = m∠9 \)[/tex]. Then by the definition of congruence, ∠5 ≅ ∠9.



Answer :

GinnyAnswer
To complete the given paragraph proof, let's insert the appropriate choices:

We know that [tex]\(<5\)[/tex] and [tex]\(<7\)[/tex] are supplementary. [tex]\(<7\)[/tex] and [tex]\(<9\)[/tex] are also supplementary because it is [tex]\(m<5 + m<7 =\)[/tex] 180 degrees and [tex]\(m<7 + m<9 =\)[/tex] 180 degrees by the definition of supplementary angles. Then, [tex]\(m<5 + m<7 = m<7 + m<9\)[/tex] by the Given. Subtract [tex]\(m<7\)[/tex] from each side and you get [tex]\(m<5 = m<9\)[/tex]. Then by the definition of congruence, [tex]\(<5 \cong\)[/tex] <9.

Thus, the final paragraph proof is:

We know that [tex]\(<5\)[/tex] and [tex]\(<7\)[/tex] are supplementary. [tex]\(<7\)[/tex] and [tex]\(<9\)[/tex] are also supplementary because it is [tex]\(m<5 + m<7 = 180\)[/tex] degrees and [tex]\(m<7 + m<9 = 180\)[/tex] degrees by the definition of supplementary angles. Then, [tex]\(m<5 + m<7 = m<7 + m<9\)[/tex] by the Given. Subtract [tex]\(m<7\)[/tex] from each side and you get [tex]\(m<5 = m<9\)[/tex]. Then by the definition of congruence, [tex]\(<5 \cong <9\)[/tex].

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