Supply the missing steps in the following paragraph proof : Given: ∠1 and ∠2 are supplementary, and ∠2 and ∠3 are supplementary
Prove: ∠1 ∠3
By the definition of supplementary angles, m∠1 + m∠2 = ___________________˚ and
m∠2 + m∠3 = ________________˚.
Then, m∠1 + m∠2 = m∠2 + m∠3 by _______________________________.
Subtract m∠2 from each side.
You get m∠1 = ___________ or ∠1 _______________.
By the definition of supplementary angles, m∠1 + m∠2 = 180˚ and m∠2 + m∠3 = 180˚.
Then, m∠1 + m∠2 = m∠2 + m∠3 by the transitive property.
Subtract m∠2 from each side.
You get m∠1 = m∠3 or ∠1 ≅ ∠3.
By the definition of supplementary angles, m∠1 + m∠2 = 180˚ and m∠2 + m∠3 = 180˚.
Then, m∠1 + m∠2 = m∠2 + m∠3 by the Transitive Property of Equality.
Subtract m∠2 from each side.
You get m∠1 = m∠3 or ∠1 ≅ ∠3 (by the definition of congruent angles).
By the definition of supplementary angles, we know that the sum of the measures of ∠1 and ∠2 is equal to 180°. Therefore, we can complete the first blank as "180°" to indicate that the sum of the measures of ∠1 and ∠2 is 180°.
Similarly, we also know that the sum of the measures of ∠2 and ∠3 is equal to 180°, as they are supplementary angles. So, we can complete the second blank as "180°" to indicate that the sum of the measures of ∠2 and ∠3 is 180°.
Since we know that both ∠1 + ∠2 = 180° and ∠2 + ∠3 = 180°, we can use the transitive property of equality to conclude that ∠1 + ∠2 = ∠2 + ∠3. Hence, we can fill in the blank in the third statement as "the transitive property of equality".
To isolate ∠1 on one side of the equation, we need to subtract ∠2 from both sides. This is because we want to find the measure of ∠1 alone. So, subtracting ∠2 from both sides gives us:
∠1 + ∠2 - ∠2 = ∠2 + ∠3 - ∠2
Simplifying this equation, ∠1 = ∠3. Therefore, we can fill in the blank in the fifth statement as "∠1" and "∠1 = ∠3" to show that the measure of ∠1 is equal to ∠3.