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 ≅
180 degrees
Symmetric property
<5
Addition property
<9
Given
Transitive property
Subtraction property
<7
90 degrees
Proven
To complete the paragraph proof, we need to use the given information and the properties of supplementary angles to prove that <5 is congruent to <9.
First, we know that <5 and <7 are supplementary, meaning they add up to 180 degrees. This is given in the problem.
We are also given that <7 and <9 are supplementary, again adding up to 180 degrees.
Now, using the definition of supplementary angles, we can write the equations:
<m<5 + m<7 = 180 degrees
<m<7 + m<9 = 180 degrees
Next, since the sum of the measures of <5 and <7 is equal to the sum of the measures of <7 and <9, we can use the addition property.
m<5 + m<7 = m<7 + m<9
Now, to prove that <5 is congruent to <9, we can use the subtraction property. By subtracting m<7 from both sides of the equation, we get:
m<5 = m<9
This shows that the measures of <5 and <9 are equal.
Finally, using the definition of congruence, we can state that <5 is congruent to <9: <5 ≅ <9.
Therefore, <5 ≅ <9 is proven.
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 given.
So, we have M<5 + m<7 = 180 degrees and m<7 + m<9 = 180 degrees by definition of supplementary angles.
Then, m<5 + m<7 = m<7 + m<9 by the transitive property.
Subtracting m<7 from each side, we get m<5 = m<9.
Then, by the definition of congruence, <5 ≅ <9.
Proven.
We know that <5 and <7 are supplementary. <7 and <9 are also supplementary because it is given. We can write this as:
m<5 + m<7 = 180 degrees (definition of supplementary angles)
m<7 + m<9 = 180 degrees (definition of supplementary angles)
We can set these two equations equal to each other since they both equal 180 degrees:
m<5 + m<7 = m<7 + m<9
Now, we can subtract m<7 from each side of the equation to isolate m<5:
m<5 = m<9
By the definition of congruence, we can conclude that <5 is congruent to <9:
<5 ≅ <9.