1 / 11

LINES IN GEOMETRY

LINES IN GEOMETRY. Unit 1 Part 2. m. n. Perpendicular Lines. Definition : Perpendicular lines are two lines that intersect to form a right angle. The symbol used for perpendicular lines is . 4 right angles are formed. . In this figure line m is perpendicular to line n.

bailey
Download Presentation

LINES IN GEOMETRY

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. LINES IN GEOMETRY Unit 1 Part 2

  2. m n Perpendicular Lines Definition: Perpendicular lines are two lines that intersect to form a right angle. The symbol used for perpendicular lines is . 4 right angles are formed. In this figure line m is perpendicular to line n. With symbols we denote, m n

  3. Conditional Statement Definition: A conditional statement is a statement that can be written in if-then form. “If _____________, then ______________.” Iftwo angles are adjacent and add up to 90 degrees, then the angles are complementary. Example: Continued……

  4. Conditional Statement - continued Conditional Statements have two parts: The hypothesis is the part of a conditional statement that follows “if” (when written in if-then form.) The hypothesis is the given information, or the condition. The conclusionis the part of an if-then statement that follows “then” (when written in if-then form.) The conclusion is the result of the given information.

  5. Three Conditional Statements • If two lines are perpendicular, then they form congruent adjacent angles. • If two lines form congruent adjacent angles, then the lines are perpendicular. The first two are converses of each other. The converse is formed by interchanging the hypothesis and the conclusion. • If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.

  6. Parallel Lines • Parallel lines are coplanar lines that do not intersect. • Arrows are used to indicate lines are parallel. • The symbol used for parallel lines is ||. In the above figure, the arrows show that line AB is parallel to line CD. With symbols we denote, .

  7. Skew Lines and Parallel Planes • Definition: Two lines are skew if they do not intersect and are not in the same plane (not coplanar). Ex: • All planes are either parallel or intersecting. • Parallel planes are two planes that do not intersect. Ex: Plane ABC and Plane EFG

  8. Examples: • Name all segments that are parallel to • Name all segments that intersect • Name all segments that are skew to • Name all planes that are parallel to plane ABC. Answers: • Segments BC, FG, & EH. • Segments DH, DC, AE & AB. • Segments CG, BF, FE, & GH. • Plane FGH.

  9. Slope of Parallel and Perpendicular Lines • The slope of the non vertical line through the points and is m = The slope of a vertical line is not defined. The slope of a horizontal line is zero. Two lines are parallel if and only if they have equal slopes. Two lines are perpendicular if and only if the product of their slopes is -1 (reciprocals and opposite signs).

  10. Examples Any line parallel to a line with slope has slope _____. Any line perpendicular to a line with slope has slope ___. Any line parallel to a line with slope 0 has slope _____. Any line perpendicular to a line with undefined slope has slope. Any line parallel to a line with slope 2 has slope _____. 0 Zero Slope 2

  11. Find the slope of the line through the given points. Examples: • (-4, 7) and (3, 7) • (3, -1) and (3, 2) • (1, -4) and (2, 5) • (-2, 5) and (1, -1)

More Related