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3-1 Lines and Angles Geometry

Explore the fundamentals of lines and angles in geometry, including parallel and perpendicular lines, types of angles, and angle relationships. Learn to identify and solve angles in various scenarios.

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3-1 Lines and Angles Geometry

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  1. 3-1 Lines and AnglesGeometry Mrs. O’Neill

  2. LINES AND ANGLES

  3. Warm Up The soccer team scored 3 goals in each of their first two games, 7 goals in the next game, and 2 goals in each of the last four games. What was the average (mean) number of goals the team scored per game? 2)

  4. Warm Up Solve the equation: = -20 = -0.8 = 9 = = -1

  5. MCC7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

  6. Formative

  7. Essential Questions How can I use the special angle relationships – supplementary, complementary, vertical, and adjacent – to write and solve equations for multi-step problems?

  8. B A D l C m PARALLEL LINES Lines that do not intersect • Notation:l || mAB|| CD

  9. Examples of Parallel Lines • Opposite sides of windows, desks, etc. • Parking spaces in parking lots • Parallel Parking • Streets in a city block

  10. m n PERPENDICULAR LINES Lines that intersect to form a right angle • Notation:m n • Key Fact: 4 right angles are formed.

  11. Ex. of Perpendicular Lines

  12. any angle less than 90º Acute Angle –

  13. a 90º angle Right Angle –

  14. any angle larger than 90º Obtuse Angle -

  15. angles that add up to 90º Complementary Angles –

  16. angles that add up to 180º Supplementary Angles –

  17. Adjacent Angles - angles that share a common vertex and ray…angles that are back to back. *Vertex – the “corner” of the angle *Ray – a line that has an endpoint on one end and goes on forever in the other direction.

  18. Congruent Angles – Angles with equal measurement A ≅B denotes that A is congruent to B.

  19. Transversal - a line that intersects a set of parallel lines t

  20. Vertical Angles Two angles that are opposite angles at intersecting lines. Vertical angles are congruent angles. t • 14 • 2  3 1 2 4 3

  21. Vertical Angles Find the measures of the missing angles t 125  ? 125  55  ? 55 

  22. t 1 2 4 3 6 5 7 8 Linear Pair Two adjacent angles that form a line. They are supplementary. (angle sum = 180) • 1+2=180 • 2+4=180 • 4+3=180 • 3+1=180 • 5+6=180 • 6+8=180 • 8+7=180 • 7+5=180

  23. Supplementary Angles/Linear Pair Find the measures of the missing angles t ? 108  72  180 - 72 ? 108 

  24. 1 2 3 4 5 6 7 8 Corresponding Angles Two angles that occupy corresponding positions when parallel lines are intersected by a transversal…same side of transversal AND same side of own parallel line. Corresponding angles are congruent angles. t • 15 • 2  6 • 3  7 • 4  8 Top Left Top Right Bottom Left Bottom Right Top Left Top Right Bottom Left Bottom Right

  25. Corresponding Angles Find the measure of the missing angle t 145  35  ? 145 

  26. Alternate Interior Angles Two angles that lie between parallel lines on opposite sides of the transversal. These angles are congruent. t • 3  6 • 4  5 1 2 3 4 5 6 7 8

  27. Alternate InteriorAngles Find the measure of the missing angle t 82  82  98  ?

  28. Alternate Exterior Angles Two angles that lie outside parallel lines on opposite sides of the transversal. They are congruent. t • 2  7 • 1  8 1 2 3 4 5 6 7 8

  29. Alternate ExteriorAngles Find the measure of the missing angle t 120  ? 120  60 

  30. Same Side Interior Angles Two angles that lie between parallel lines on the same sides of the transversal. These angles are supplementary. t • 3 +5 = 180 • 4 +6 = 180 1 2 3 4 5 6 7 8 *Also known as Consecutive Interior Angles

  31. Same Side InteriorAngles Find the measure of the missing angle t 180 - 135 135  45  ?

  32. Same Side Exterior Angles Two angles that lie outside parallel lines on the same side of the transversal. These angles are supplementary. t • 1 +  7 = 180 • 2 + 8 = 180 1 2 3 4 5 6 7 8 *Also known as Consecutive Exterior Angles

  33. Same Side ExteriorAngles Find the measure of the missing angle t 135  180 - 135 ? 45 

  34. 1,5 3,7 2,6 4,8 3,6 5,4 1,8 2,7 3,5 4,6 1,7 2,8

  35. equivalent equivalent equivalent supplementary supplementary

  36. 112º 68º 68º 112º 112º 112º 68º 68º

  37. Closing What is a transversal? Name the types of equivalent angles. Name the types of supplementary angles.

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