Special Lines

and Angles

MGSE8.G.1 Verify

experimentally the properties of rotations,

reflections, and translations:

a. Lines are taken to lines,

and line segments to line

segments of the same

length. b. Angles are taken

to angles of the same

measure. c. Parallel lines are taken to parallel lines.

Inquiry Lab

When lines, segments, or rays intersect, they form angles. If the angles formed by two intersecting lines are equal to 90°, the lines are perpendicular lines.

Some lines in the same plane do not intersect at all. These lines are parallel lines. Segments and rays that are part of parallel lines are also parallel.

The symbol means “is parallel to.” The symbol means “is perpendicular to.”

Reading Math

Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.

Reading Math

If the sum of the measures of two angles is 90°, then the angles are

complementary angles.

If the sum of the measures of two angles is 180°, then the angles are

supplementary angles.

Adjacent angles have a common vertex and a common side, but no common interior points. Angles 2 and 3 in the diagram are adjacent. Adjacent angles formed by two intersecting lines are supplementary

Vertical angles are the opposite angles formed by two intersecting lines. When two lines intersect, two pairs of vertical angles are formed. Vertical angles have the same measure, so they are congruent.

A transversal is a line that intersects two or more lines. Line t is a transversal. When the lines that are intersected are parallel, four pairs of corresponding angles are formed.

Corresponding angles are on the same side of the transversal and are both above or both below the parallel lines. Angles 1 and 5 are corresponding angles. Corresponding angles are congruent.

Special angles relationships created by a transversal.

The same-side interior angle theorem

states that when two lines that are parallel

are intersected by a transversal line, the

same-side interior angles that are formed

are supplementary, or add up to 180

degrees.

Same-side exterior angles theorem states

that when two lines that are parallel are

intersected by a transversal line, the

same-side exterior angles that are formed

are supplementary, or add up to 180

degrees

Line n line p. Find the measure of the angle.

Additional Example 2A: Using Angle Relationships to

Find Angle Measures

2

2 and the 130° angle are vertical angles. Since vertical angles are congruent, m2 = 130°.

Line n line p. Find the measure of the angle.

Additional Example 2B: Using Angle Relationships to

Find Angle Measures

33 and the 50° angle are acute angles. Since all of the acute angles in the figure are congruent, m3 = 50°.

Line n line p. Find the measure of the angle.

Additional Example 2C: Using Angle Relationships to

Find Angle Measures

4

4 is an obtuse angle. Since all of the obtuse angles in the figure are congruent, m4 = 130°.