2020年7月6日 · The alternate interior angles theorem states that when two parallel lines are cut by a transversal, the resulting angles produced are a pair of congruent alternate interior angles. Given the image attached below, both line k and line l are parallel to each other and also, line t is the transversal, therefore the resulting congruent alternate ...

2018年12月6日 · D. Converse Alternate Interior Angles Theorem: This states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel. In this context, if the proof is dealing with angles formed by a transversal cutting through two parallel lines, the missing reason is likely to be related to the ...

2024年1月30日 · Now, the converse alternate interior angles theorem states that if two lines are intersected by a transversal and the alternate interior angles are congruent, then the lines are parallel. In the context of the proof, the missing reason is …

2023年9月11日 · When we apply the Alternate Interior Angles Theorem, we note that when a transversal intersects two parallel lines, the alternate interior angles formed are congruent. The converse then allows us to reason that if these angles are indeed found to be congruent, we can conclude that the two lines must be parallel.

Alternate Interior Angles Theorem, Converse of Corresponding Angles Postulate, Given, Reflexive Property, Transitive Property, Vertical Angles Theorem Statement Reasons Transversal t cuts line l and line m. 1. Given ∠2 ≅ ∠7 2. ∠2 ≅ ∠3 3. ∠3 ≅ ∠7 4. l ║m 5.

2017年11月8日 · The missing reason at step 5 is that when two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. This is known as the Converse of the Alternate Interior Angles Theorem, which perfectly suits the context of our proof. Hence, the correct answer is (D) Converse Alternate Interior Angles ...

2020年9月15日 · Given that e parallel f and g is a transversal, we know that angle 4 is-congruent-to angle 5 by the alternate interior angles theorem. we also know that angle 1 is-congruent-to angle 4 and angle 5 is-congruent-to angle 8 by the _____. therefore, angle 1 is-congruent-to angle 8 by the substitution property. corresponding angles theorem alternate ...

2020年10月1日 · Therefore, the correct reasoning to justify the parallel nature of lines j and k is the Converse of the Alternate Exterior Angles Theorem, as the angles formed are not interior but are corresponding angles in the context of the transversal m. Thus, the answer is converse alternate exterior angles theorem.

2024年1月25日 · Identifying Congruent Angles: The proof correctly identifies that ∠ ZRP ≅ ∠ RPQ and ∠ QR Y ≅ ∠ PQR due to the Alternate Interior Angles Theorem. This is based on the understanding that when a line intersects two parallel lines, the pairs of angles created by that intersection are congruent.

2021年6月23日 · A) Alternate Interior Angles Theorem B) Corresponding Angles Theorem C) Alternate Exterior Angles Theorem D) Same-Side Interior Angles Theorem Community Answer This answer has a 4.9 rating