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Geometry Lines and Angles

Geometry Lines and Angles. Warm Up. Find the circumference and area of each circle. 1). 2). 80 cm. 3.8 m. Parallel, perpendicular and skew lines.

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Geometry Lines and Angles

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  1. GeometryLines and Angles CONFIDENTIAL

  2. Warm Up Find the circumference and area of each circle. 1) 2) 80 cm 3.8 m CONFIDENTIAL

  3. Parallel, perpendicular and skew lines Pairs of lines can relate to each other in four different ways: intersecting lines, parallel lines, perpendicular lines and skew lines. These concepts are useful for understanding and solving various geometry problems. CONFIDENTIAL

  4. Parallel lines (||)are lines that never intersect i.e. they are coplanar. The distance between the two lines is fixed and the two lines go in the same direction. In the figure, AB || EF and EG || FH. A B E F C D G H Parallel, perpendicular and skew lines CONFIDENTIAL

  5. A B E F C D G H Parallel, perpendicular and skew lines Perpendicular lines (|)are lines that intersect at one point and form a 90° angle i.e. two different straight lines on the same plane in two different directions who meet each other at only right angles are called Perpendicular Lines. In the figure, AB | AE and EG | GH. CONFIDENTIAL

  6. Skew lines are not coplanar. Skew lines only happen in space. Skew lines never intersect because they are not on the same plane. Skew lines are difficult to draw because they exist in the three dimensional space. In the figure, AB and EG are skew. A B E F C D G H Parallel, perpendicular and skew lines CONFIDENTIAL

  7. A B E F C D G H Parallel, perpendicular and skew lines Parallel planes are planes that do not intersect. In the figure, plane ABE || planeCDG. CONFIDENTIAL

  8. A pair of parallel segments. • KN || PS B) A pair of skew segments. LM || RS K L N M C) A pair of perpendicular segments. MR | RS P Q S R Identifying types of lines and planes Identify each of the following: D) A pair of parallel planes. plane KPS || plane LQR. CONFIDENTIAL

  9. AB is perpendicular to CL and  CIB is 90° • KE intersects IB at point J • GH is parallel to AB • KD is perpendicular to MH and  KLH is 90° • IL intersects JM at point K • EF intersects GL at point M, intersects IL at point K and IB at point J Referring to the figure, we can conclude: CONFIDENTIAL

  10. C D B E G H F J Now you try! Identify each of the following: 1a) A pair of parallel segments 1b) A pair of skew segments 1c) A pair of perpendicular segments 1d) A pair of parallel planes CONFIDENTIAL

  11. Angle pairs formed by a transversal A transversal is a line that intersects two coplanar lines at two different points. The traversal t and the other two lines r and s form eight angles. exterior angles interior angles exterior angles CONFIDENTIAL

  12. Corresponding angles are created where a transversal crosses other (usually parallel) lines. The corresponding angles are the ones at the same location at each intersection i.e. angle 1 and angle 5. Corresponding angles CONFIDENTIAL

  13. Alternate interior angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles are inside the parallel lines, and on opposite sides of the transversal i.e. angle 3 and angle 5. Alternate interior angles CONFIDENTIAL

  14. Alternate exterior angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles are outside the parallel lines, and on opposite sides of the transversal i.e. angle 1 and angle 7. Alternate exterior angles CONFIDENTIAL

  15. Same side interior angles crosses two (usually parallel) lines. Each pair of interior angles are inside the parallel lines, and on the same side of the transversal. i.e. angle 3 and angle 6. Same side interior angles CONFIDENTIAL

  16. 1 2 4 3 5 6 8 7 Classifying pairs of angles Give an example of each angle pair. A) Corresponding angles Angle 4 and angle 8 B) Alternate interior angles Angle 4 and angle 6 C) Alternate exterior angles Angle 2 and angle 8 D) Same side interior angles Angle 4 and angle 5 CONFIDENTIAL

  17. 1 2 3 4 5 6 7 8 Now you try! Give an example of each angle pair. 2a) Corresponding angles 2b) Alternate interior angles 2c) Alternate exterior angles 2d) Same side interior angles CONFIDENTIAL

  18. 4 l 1 2 3 5 6 n m Identifying angle pairs and transversals Identify the transversal and classify each angle pair. A) Angle 1 and angle 5 transversal: n;Alternate interior angles B) Angle 3 and angle 6 transversal: m;Correspondingangles C) Angle 1 and angle 4 transversal: l;Alternate exteriorangles CONFIDENTIAL

  19. 3) Identify the transversal and classify the angle pair 2 and 5 in the diagram. 4 l 1 2 3 5 6 m Now you try! n CONFIDENTIAL

  20. B C A D F G E H Assessment Identify each of the following: 1) A pair of perpendicularsegments 2) A pair of skew segments 3) A pair of parallelsegments 4) A pair of parallel planes CONFIDENTIAL

  21. 6 2 3 7 5 1 4 8 Give an example of each angle pair. 5) Alternate interior angles 6) Alternate exterior angles 7) Corresponding angles 8) Same side interior angles CONFIDENTIAL

  22. m 1 2 n 4 5 3 p Identify the transversal and classify each angle pair. 9) Angle 1 and angle 2 10) Angle 2 and angle 3 11) Angle 2 and angle 4 12) Angle 4 and angle 5 CONFIDENTIAL

  23. Parallel lines (||)are lines that never intersect i.e. they are coplanar. The distance between the two lines is fixed and the two lines go in the same direction. In the figure, AB || EF and EG || FH. A B E F C D G H Let’s review Parallel, perpendicular and skew lines CONFIDENTIAL

  24. A B E F C D G H Parallel, perpendicular and skew lines Perpendicular lines (|)are lines that intersect at one point and form a 90° angle i.e. two different straight lines on the same plane in two different directions who meet each other at only right angles are called Perpendicular Lines. In the figure, AB | AE and EG | GH. CONFIDENTIAL

  25. Skew lines are not coplanar. Skew lines only happen in space. Skew lines never intersect because they are not on the same plane. Skew lines are difficult to draw because they exist in the three dimensional space. In the figure, AB and EG are skew. A B E F C D G H Parallel, perpendicular and skew lines CONFIDENTIAL

  26. A B E F C D G H Parallel, perpendicular and skew lines Parallel planes are planes that do not intersect. In the figure, plane ABE || planeCDG. CONFIDENTIAL

  27. Angle pairs formed by a transversal A transversal is a line that intersects two coplanar lines at two different points. The traversal t and the other two lines r and s form eight angles. exterior angles interior angles exterior angles CONFIDENTIAL

  28. Corresponding angles are created where a transversal crosses other (usually parallel) lines. The corresponding angles are the ones at the same location at each intersection i.e. angle 1 and angle 5. Corresponding angles CONFIDENTIAL

  29. Alternate interior angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles are inside the parallel lines, and on opposite sides of the transversal i.e. angle 3 and angle 5. Alternate interior angles CONFIDENTIAL

  30. Alternate exterior angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles are outside the parallel lines, and on opposite sides of the transversal i.e. angle 1 and angle 7. Alternate exterior angles CONFIDENTIAL

  31. Same side interior angles crosses two (usually parallel) lines. Each pair of interior angles are inside the parallel lines, and on the same side of the transversal. i.e. angle 3 and angle 6. Same side interior angles CONFIDENTIAL

  32. You did a great job today! CONFIDENTIAL

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