Question
Given: w ∥ x and y is a transversal.
Prove: ∠3 and ∠5 are supplementary.
Parallel and diagonal lines w and x are cut by horizontal transversal y. On line w where it intersects with line y, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 3, 4, 2. On line x where it intersects with line y, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 7, 8, 6.
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
Prove: ∠3 and ∠5 are supplementary.
Parallel and diagonal lines w and x are cut by horizontal transversal y. On line w where it intersects with line y, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 3, 4, 2. On line x where it intersects with line y, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 7, 8, 6.
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
Answers
GPT-4o mini
To complete the proof, we can fill in the drop-down menus as follows:
**Given that \( w \parallel x \) and \( y \) is a transversal, we know that \( \angle 1 \cong \angle 5 \) by the** **Corresponding Angles Postulate.** **Therefore, \( m\angle 1 = m\angle 5 \) by the definition of congruent angles. We also know that, by definition, \( \angle 3 \) and \( \angle 1 \) are a linear pair so they are supplementary by the** **Linear Pair Postulate.** **By the** **definition of supplementary angles, \( m\angle 3 + m\angle 1 = 180 \). 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.**
This proof structure takes advantage of the properties of parallel lines and transversals, utilizing the corresponding angles and linear pair postulates to establish that angles \( \angle 3 \) and \( \angle 5 \) are indeed supplementary.
**Given that \( w \parallel x \) and \( y \) is a transversal, we know that \( \angle 1 \cong \angle 5 \) by the** **Corresponding Angles Postulate.** **Therefore, \( m\angle 1 = m\angle 5 \) by the definition of congruent angles. We also know that, by definition, \( \angle 3 \) and \( \angle 1 \) are a linear pair so they are supplementary by the** **Linear Pair Postulate.** **By the** **definition of supplementary angles, \( m\angle 3 + m\angle 1 = 180 \). 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.**
This proof structure takes advantage of the properties of parallel lines and transversals, utilizing the corresponding angles and linear pair postulates to establish that angles \( \angle 3 \) and \( \angle 5 \) are indeed supplementary.