Question

(a) ángulos alternos externos: ∠□ y ∠□ (b) ángulos alternos internos: ∠□ y ∠□ (c) ángulos correspondientes: ∠□ y ∠□

Explanation:

Step1: Recall the definitions

• Alternate exterior angles: They are on the outer side of the two parallel lines \(m\) and \(n\) and on the opposite side of the transversal \(h\).
• Alternate interior angles: They are on the inner side of the two parallel lines \(m\) and \(n\) and on the opposite side of the transversal \(h\).
• Corresponding angles: They are in the same relative position with respect to the parallel lines \(m\), \(n\) and the transversal \(h\).

Step2: Identify the pairs

• For (a) Alternos externos (\( \angle1\) and \( \angle8\), \( \angle2\) and \( \angle7\)):
• \( \angle1\) and \( \angle8\): \( \angle1\) is above line \(m\) and \( \angle8\) is below line \(n\), on the opposite side of transversal \(h\).
• \( \angle2\) and \( \angle7\): \( \angle2\) is above line \(m\) and \( \angle7\) is below line \(n\), on the opposite side of transversal \(h\).
• For (b) Alternos internos (\( \angle3\) and \( \angle5\), \( \angle4\) and \( \angle6\)):
• \( \angle3\) and \( \angle5\): \( \angle3\) is below line \(m\) and \( \angle5\) is above line \(n\), on the opposite side of transversal \(h\).
• \( \angle4\) and \( \angle6\): \( \angle4\) is below line \(m\) and \( \angle6\) is above line \(n\), on the opposite side of transversal \(h\).
• For (c) Correspondientes (\( \angle1\) and \( \angle5\), \( \angle2\) and \( \angle6\), \( \angle3\) and \( \angle7\), \( \angle4\) and \( \angle8\)):
• \( \angle1\) and \( \angle5\): Both are in the upper - left position with respect to their respective parallel lines and the transversal.
• \( \angle2\) and \( \angle6\): Both are in the upper - right position with respect to their respective parallel lines and the transversal.
• \( \angle3\) and \( \angle7\): Both are in the lower - right position with respect to their respective parallel lines and the transversal.
• \( \angle4\) and \( \angle8\): Both are in the lower - left position with respect to their respective parallel lines and the transversal.

Answer:

(a) \( \angle1\) y \( \angle8\), \( \angle2\) y \( \angle7\)
(b) \( \angle3\) y \( \angle5\), \( \angle4\) y \( \angle6\)
(c) \( \angle1\) y \( \angle5\), \( \angle2\) y \( \angle6\), \( \angle3\) y \( \angle7\), \( \angle4\) y \( \angle8\)