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Section 3.1 Lines and Angles
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Perpendicular Lines Intersecting lines that form right angles Symbol XS SR
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Parallel Lines Two lines that are coplanar and do not intersect Symbol: II XY II UZ
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Skew Lines Lines do not intersect and are not coplanar
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Example Is XY parallel or skew to RV? XY II RV
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Parallel planes Two planes that do not intersect
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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.
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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.
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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
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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
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Examples: Solve for x Ex 3. 60° x ANSWER: 60 + x = 90 -60 -60 x = 30
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Example 4 x 55° ANSWER: x + 55 = 90 -55 -55 x = 35
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Example 5 27° (2x-9)° ANSWER: 2x – 9 + 27 = 90 2x +18 = 90 2x = 72 x = 36
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Theorem 3.3 If 2 lines are perpendicular, then they intersect to form four right angles. m l
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Complete Try it! Problems #1-8
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Transversal A line that intersects two or more coplanar lines at different points. transversal
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Vertical Angles Formed by the intersection of two pairs of opposite rays 12 34 5 6 78
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Linear Pair Adjacent angles that are supplementary 12 34 5 6 78
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Corresponding Angles Occupy corresponding positions. 12 34 5 6 78
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Alternate Exterior Angles Lie outside the 2 lines on opposite sides of the transversal. 12 34 5 6 78
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Alternate Interior Angles Lie between the 2 lines on opposite sides of the transversal. 12 34 5 6 78
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Consecutive Interior Angles (Same side interior angles) Lie between the 2 lines on the same side of the transversal. 12 34 5 6 78
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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 & 5 12 34 56 7 8
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