Complete the following paragraph proof. (You may use the choices more than once and you may not use all the choices)
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 it is m<5 + m<7 =
and m< 7 + m<9 = , by definition of supplementary angles. Then, m<5 + m<7 = m<7 + m<9 by the
. Subtract m<7 from each side and you get m<5 = m<9. Then by the definition of congruence, <5
is congruent to <9.
<9. Therefore, <5 is congruent to <9, which proves that <5 <9.
is congruent to <9. Therefore, we have proven that <5 <9.
To complete the paragraph proof, we can use the following statements and reasons:
1. <5 and <7 are supplementary - Given
2. <7 and <9 are supplementary - Given
3. m<5 + m<7 = 180° - Definition of supplementary angles
4. m<7 + m<9 = 180° - Definition of supplementary angles
5. m<5 + m<7 = m<7 + m<9 - Transitive property of equality
6. Subtract m<7 from each side - Subtraction property of equality
7. m<5 = m<9 - Simplification
8. <5 ≅ <9 - Definition of congruence
9. <5 <9 - Congruent angles are also considered to be "less than" each other.
Thus, we have successfully completed the paragraph proof by providing the necessary statements and reasons to show that <5 <9.