Transversal postulate: tranversal and parallel lines

If a transversal intersects two parallel lines then:
(a) All corresponding angles are equal. Angle1 = Angle5
(b) Each pair of alternate angles are equal (congruent). Angle1 = Angle3
(b) the interior angles on the same side of the transversal are supplementary. Supplementary angles are any two angles whose sum is 180 degrees. Angle1 + Angle2 = 180º


Exercise: r line is parallel to s line. The angle1 measures 60 degrees.
Find the measures of the other seven angles in the figure (right).

Clic on the picture below to see a graphic proof.

Solution:
Angle2 = 120 degrees since it is supplementary to angle 1.
Angle3 = 60 degrees since Angle1 and Angle3 are vertical angles.
Vertical angles are two nonadjacent angles (opposite angles) formed by two intersecting lines.
Angle4 = 120 degrees since it is supplementary to angle1.
Angle5 = angle1 = 60º, by the Transversal Postulate.
Angle6 = angle2 = 120º,
angle7 = angle3 = 60º, and
angle8 = angle4 = 120º, by the Transversal Postulate.

Vocabulary: (to) intersect = intersectar, cortar
postulate= postulado, enunciado intuitivo que no se demuestra.
(to) measure= medir
proof= demostración