Question

if the corresponding angles formed by the transversal of two lines are congrunt then the. two lines are parallel , converse the sentence​

Answer 1

Answer:

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In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points. Transversals play a role in establishing whether two other lines in the Euclidean plane are parallel. The intersections of a transversal with two lines create various types of pairs of angles: consecutive interior angles, corresponding angles, and alternate angles. By Euclid's parallel postulate, if the two lines are parallel, consecutive interior angles are supplementary, corresponding angles are equal, and alternate angles are equal.

Step-by-step explanation:

A transversal produces 8 angles, as shown in the graph at the above left:

4 with each of the two lines, namely α, β, γ and δ and then α1, β1, γ1 and δ1; and

4 of which are interior (between the two lines), namely α, β, γ1 and δ1 and 4 of which are exterior, namely α1, β1, γ and δ.

A transversal that cuts two parallel lines at right angles is called a perpendicular transversal. In this case, all 8 angles are right angles [1]

When the lines are parallel, a case that is often considered, a transversal produces several congruent and several supplementary angles. Some of these angle pairs have specific names and are discussed below:[2][3]corresponding angles, alternate angles, and consecutive angles.Corresponding angles are the four pairs of angles that:

have distinct vertex points,

lie on the same side of the transversal and

one angle is interior and the other is exterior.

Two lines are parallel if and only if the two angles of any pair of corresponding angles of any transversal are congruent (equal in measure).

This follows directly from Euclid's parallel postulate. Further, if the angles of one pair are congruent, then the angles of each of the other pairs are also congruent. In our images with parallel lines, corresponding angle pairs are: α=α1, β=β1, γ=γ1 and δ=δ1.