Lines Cut by a Transversal Answers

A: [___]

Angle 3 is congruent to angle 6. ✔ Angle 3 is congruent to angle 7. Angle 6 is congruent to angle 7. Angle 4 is congruent to angle 5.

congruent supplements theoremdefinition of a linear pair✔ definition of supplementary angleslinear pair postulate

What is the value of x?[___]

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.

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Use the drop-down menus to complete the paragraph proof showing that alternate interior angles are congruent. We know that lines a and b are parallel and that line c is a transversal because that is given. We can tell that angles 2 and 5 are congruent because [___] angles are congruent. Angles 5 and 7 are congruent because [___] angles by parallel lines cut by a transversal are congruent. Therefore, angles 2 and 7 are congruent based on the [___].

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