Question

Proving Same Side Interior Angles Supplementary Given: w // x and y is a transversal. Prove: \(\angle 3\) and \(\angle 5\) are supplementary. w x 1 3 5 7 2 4 6 8 y Use the drop-down menus to complete the proof. Given that w // x and y is a transversal, we know that \(\angle 1 \cong \angle 5\) by the Therefore, \(m\angle 1 = m\angle 5\) by the definition of congruent. We also know that, by definition, \(\angle 3\) and \(\angle 1\) are a linear pair so they are supplementary by the By the \(m\angle 3 + m\angle 1 =\ 180. Now we can substitute \(m\angle 5\) for \(m\angle 1\) to get \(m\angle 3 + m\angle 5 = 180\). Therefore, by the definition of supplementary angles, \(\angle 3\) and \(\angle 5\) are supplementary.

          Proving Same Side Interior Angles Supplementary
Given: w // x and y is a transversal.
Prove: \(\angle 3\) and \(\angle 5\) are supplementary.
w
x
1
3
5
7
2
4
6
8
y
Use the drop-down menus to complete the proof.
Given that w // x and y is a transversal, we know that
\(\angle 1 \cong \angle 5\) by the
Therefore, \(m\angle 1 = m\angle 5\) by the definition of
congruent. We also know that, by definition, \(\angle 3\) and
\(\angle 1\) are a linear pair so they are supplementary by the
By the
\(m\angle 3 + m\angle 1 =\
180. Now we can substitute \(m\angle 5\) for \(m\angle 1\) to get
\(m\angle 3 + m\angle 5 = 180\). Therefore, by the definition of
supplementary angles, \(\angle 3\) and \(\angle 5\) are supplementary.

Proving Same Side Interior Angles Supplementary
Given: w // x and y is a transversal.
Prove: ∠ 3 and ∠ 5 are supplementary.
w
x
1
3
5
7
2
4
6
8
y
Use the drop-down menus to complete the proof.
Given that w // x and y is a transversal, we know that
∠ 1 ≅∠ 5 by the
Therefore, m∠ 1 = m∠ 5 by the definition of
congruent. We also know that, by definition, ∠ 3 and
∠ 1 are a linear pair so they are supplementary by the
By the
m∠ 3 + m∠ 1 =180. Now we can substitute m∠ 5 for m∠ 1 to get
m∠ 3 + m∠ 5 = 180. Therefore, by the definition of
supplementary angles, ∠ 3 and ∠ 5 are supplementary.

Added by Carolyn W.

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