Question

What does it mean by type of angles and relationship between the angles if the line are parallel ?

Answer 1

Where two lines cross, four (4) angles are formed. Two adjacent angles that share a vertex can be called a "linear pair." Two non-adjacent angles that have the same vertex and the same lines for sides, are called "vertical angles."

Where a transversal crosses two parallel lines, eight (8) angles are formed, four (4) at each intersection. In addition to the above angle types, there are other relationships that can be described.

Angles can be called corresponding, if they are in the same location relative to the intersection point (both on the north-east corner, for example). Angles are interior if they are between the parallel lines; exterior of they are not. They get the additional descriptor of opposite, if they are on opposite sides of the transversal.

If the angles are not opposite, and share a side but not a vertex, they can be called adjacent. (Only interior angles can be adjacent, one pair on either side of the transversal.)

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With the above definitions in mind, several relationships arise where a transversal crosses parallel lines. (Types of angles are italicized.) Two examples of each type are listed by angle numbers. Angles 1 and 2 are a linear pair, for example.

Angles of a linear pair are supplementary. (1, 2), (5, 7)

Vertical angles are congruent. (1, 4), (6, 7)

Adjacent angles are supplementary. (3, 5), (4, 6)

Corresponding angles are congruent. (1, 5), (4, 8)

Opposite interior angles are congruent. (3, 6), (4, 5)

Opposite exterior angles are congruent. (1, 8), (2, 7)