Using what you know about angle pairs formed by parallel lines and a​ transversal, how are angle∠​1, angle∠​2, angle∠​3, and angle∠4 related in the​ trapezoid? Explain.

Question

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Part 1
angle∠1 and angle∠enter your response here are
▼
congruent
supplementary
complementary
and angle∠2 and angle∠enter your response here are
▼
complementary
congruent
supplementary
because they are
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same-side exterior angles.
same-side interior angles.
corresponding angles.
alternate exterior angles.

Answer 1

To analyze the angle relationships in a trapezoid formed by parallel lines and a transversal, let's denote:

• Angle ∠1 and Angle ∠2 as the angles formed on one side of the transversal.
• Angle ∠3 and Angle ∠4 as the angles formed on the other side of the transversal.

In the case of a trapezoid with parallel sides, the following relationships hold:

1. Angle ∠1 and Angle ∠2 are at the top of the trapezoid formed by the transversal crossing the parallel sides. Since these angles are on the same side of the transversal and correspond to the parallel lines, they are classified as same-side interior angles.

2. Angle ∠3 and Angle ∠4 are located at the bottom of the trapezoid, also formed by the transversal. Similarly, these angles are also same-side interior angles.

Now, since we know that:

• Same-side interior angles are supplementary when they are formed by a transversal across two parallel lines.

Applying these principles to your question:

• Angle ∠1 and Angle ∠2 are supplementary because they are same-side interior angles.
• Angle ∠3 and Angle ∠4 are also supplementary for the same reason.

In summary:

• Angle ∠1 and Angle ∠2 are supplementary.
• Angle ∠3 and Angle ∠4 are also supplementary.
• They are classified as same-side interior angles.

Thus, you could conclude that:

• Angle ∠1 and angle ∠2 are supplementary because they are same-side interior angles.
• Angle ∠3 and angle ∠4 are supplementary because they are same-side interior angles.