Given: <5 and <7 are supplementary. <7 and <9 are also supplementary
To Prove: <5 ≅ <9
Proof:
1. <5 and <7 are supplementary (Given)
2. <7 and <9 are supplementary (Given)
3. <5 + <7 = 180° (Definition of supplementary angles)
4. <7 + <9 = 180° (Definition of supplementary angles)
5. <5 + <7 = <7 + <9 (Transitive property of equality)
6. <5 = <9 (Subtraction property of equality)
7. <5 ≅ <9 (Definition of congruence)
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
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
(5 points)
≅ ≅
1 answer