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3-1 Lines and Angles Geometry

3-1 Lines and Angles Geometry. Mrs. O’Neill. LINES AND ANGLES. 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). Warm Up.

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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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