Section 3.1 Lines and Angles

Perpendicular Lines Intersecting lines that form right angles Symbol XS SR

Parallel Lines Two lines that are coplanar and do not intersect Symbol: II XY II UZ

Skew Lines Lines do not intersect and are not coplanar

Example Is XY parallel or skew to RV? XY II RV

Parallel planes Two planes that do not intersect

Parallel Postulate If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.

Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.

Theorem 3.1 If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular Ex 1 ABC D m<ABD = m<DBC and a linear pair, BD AC

Theorem 3.2 If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. Ex. 2 H F G J <FGJ is complementary to <JGH

Examples: Solve for x Ex 3. 60° x ANSWER: 60 + x = x = 30

Example 4 x 55° ANSWER: x + 55 = x = 35

Example 5 27° (2x-9)° ANSWER: 2x – = 90 2x +18 = 90 2x = 72 x = 36

Theorem 3.3 If 2 lines are perpendicular, then they intersect to form four right angles. m l

Complete Try it! Problems #1-8

Transversal A line that intersects two or more coplanar lines at different points. transversal

Vertical Angles Formed by the intersection of two pairs of opposite rays

Linear Pair Adjacent angles that are supplementary

Corresponding Angles Occupy corresponding positions

Alternate Exterior Angles Lie outside the 2 lines on opposite sides of the transversal

Alternate Interior Angles Lie between the 2 lines on opposite sides of the transversal

Consecutive Interior Angles (Same side interior angles) Lie between the 2 lines on the same side of the transversal

Angle Relationships: Name a pair of angles Corresponding –Ex. 1 & 5 Alternate Exterior –Ex. 2 & 7 Alternate Interior –Ex. 4 & 5 Consecutive Interior –Ex. 3 &