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Learn to identify and describe geometric figures.

7-1. Points, Lines, and Planes. Course 2. Learn to identify and describe geometric figures. Learn to identify angles and parts of angles. Learn to identify parallel, perpendicular, and skew lines, and angles formed by a transversal. 7-1. Points, Lines, and Planes. XY , or YX.

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Learn to identify and describe geometric figures.

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  1. 7-1 Points, Lines, and Planes Course 2 Learn to identify and describe geometric figures. Learn to identify angles and parts of angles. Learn to identify parallel, perpendicular, and skew lines, and angles formed by a transversal.

  2. 7-1 Points, Lines, and Planes XY, or YX Helpful Hint Use two points on the line to name a line. X Y A number line is an example of a line. Course 2 A point is an exact location in space. It is usually represented as a dot, but it has no size at all point A Use a capital letter to name a point. • A A lineis a straight path that extends without end in opposite directions.

  3. 7-1 Points, Lines, and Planes GH Name the endpoint first when naming a ray. G H LM, or ML Use the endpoints to name a line segment. L M Course 2 A ray is a part of a line. It has one endpoint and extends without end in one direction. A line segmentis part of a line. or a ray that extends from one endpoint to another.

  4. 7-1 Points, Lines, and Planes Q S R Helpful Hint A coordinate plane is an example of a plane. Course 2 A plane is a perfectly flat surface that extends infinitely in all directions. plane QRS Use three points in any order, not on the same line, to name a plane.

  5. 7-1 Points, Lines, and Planes Course 2 Additional Example 1: Identifying Points, Lines, and Planes Identify the figures in the diagram. D E F A. three points D, E, and F Choose any two points on a line to name the line. B. two lines DE, DF Choose any three points, not on the same line, in any order. C. a plane plane DEF

  6. 7-1 Points, Lines, and Planes Course 2 Try This: Example 2 Identify the figures in the diagram. D C A. three rays Name the endpoint of a ray first. B A BC, CA, BD B. three line segments Use the endpoints in any order to name a segment. BA, CA, BD

  7. 7-1 Points, Lines, and Planes Course 2 Figures are congruent if they have the same shape and size. If you place one on top of the other, they match exactly. Line segments are congruent if they have the same length. Tick marks are used to indicate congruent line segments. In the illustration below, segments that have the same number of tick marks are congruent. Line segments AB and BC are congruent (one tick mark), and line segments MN and OP are congruent (two tick marks). B 5 ft N O 20 m 20 m 3 ft 3 ft C P A M 8 ft 16 m

  8. 7-1 Points, Lines, and Planes A B AB CD E F ACBD C D BF DF EC AE Reading Math The symbol means “is congruent to.” Course 2 Additional Example 3: Identifying Congruent Line Segments Identify the line segments that are congruent. One tick mark Two tick marks Three tick marks

  9. 7-2 Angles A Vertex 1 B C Course 2 An angleis formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is is the vertex. You can name an angle in three ways: • with the capital letter at the vertex: B, •with the number inside the angle: 1, •with three capital letters so that the letter at the vertex is in the middle: CBA ABC or

  10. 7-2 Angles The measure of XYZ is 122°, or m XYZ = 122°. Course 2 Angles are measured in degrees (°). You can use a protractor to measure an angle.

  11. 7-2 Angles Course 2 An angle’s measure determines the type of angle it is. A right angle is an angle that that measures exactly 90°. The symbol indicates a right angle An acute angle is an angle that measures less than 90° Anobtuse angle is an angle that measures more than 90° but less than180° A straightangle is an angle that measures 180°

  12. 7-2 Angles Course 2 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.

  13. 7-2 Angles m OMP = 30° and m OMR = 60° N Q 60° 90° P OMP and OMR are complementary. M 30° O 60° R Course 2 Additional Example 3A: Identifying Complementary and Supplementary Angles Use the figure to name the following. A. one pair of complementary angles Since 30° + 60° = 90°,

  14. 7-2 Angles m QMP = 90° and m PMR = 30° + 60° = 90° N Q 60° 90° P Since 90° + 90° = 180°, M 30° O 60° R QMP and PMR are supplementary. Course 2 Try This: Example 3B Use the figure to name the following. B. one pair of supplementary angles

  15. 7-3 Parallel and Perpendicular Lines Course 2 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. Skew lines do not intersect, and yet they are also not parallel. They lie in different planes.

  16. 7-3 Parallel and Perpendicular Lines Reading Math The symbol means “is parallel to.” The symbol means “is perpendicular to.” Course 2

  17. 7-3 Parallel and Perpendicular Lines Course 2 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.

  18. 7-3 Parallel and Perpendicular Lines Course 2 A transversalis a line that intersects two or more lines. Eight angles are formed when a transversal intersects two lines. When those two lines are parallel, all of the acute angles formed are congruent, and all of the obtuse angles formed are congruent. These obtuse and acute angles are supplementary. 1 2 3 4 5 6 7 8

  19. 7-3 Parallel and Perpendicular Lines Course 2 Reading Math Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.

  20. 7-3 Parallel and Perpendicular Lines 2 and the 130° angle are vertical angles. Since vertical angles are congruent, m 2 = 130°. Course 2 Additional Example 2A: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. 2 A.

  21. 7-3 Parallel and Perpendicular Lines 3 and the 50° angle are acute angles. Since all of the acute angles in the figure are congruent, m 3 = 50°. Course 2 Additional Example 2B: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. 3 B.

  22. 7-3 Parallel and Perpendicular Lines 4 is an obtuse angle. Since all of the obtuse angles in the figure are congruent, m 4 = 130°. Course 2 Additional Example 2C: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. 4 C.

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