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Transcript
3-1 Lines and Angles Geometry LINES AND ANGLES Warm Up 2) 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? Warm Up Solve the equation: = -20 = -0.8 = 9 = -1 = MCC7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. Formative Essential Questions How can I use the special angle relationships – supplementary, complementary, vertical, and adjacent – to write and solve equations for multi-step problems? PARALLEL LINES Lines that do not intersect B l A m D C • Notation: l || m AB || CD Examples of Parallel Lines • • • • Opposite sides of windows, desks, etc. Parking spaces in parking lots Parallel Parking Streets in a city block PERPENDICULAR LINES Lines that intersect to form a right angle m n • Notation: m n • Key Fact: 4 right angles are formed. Ex. of Perpendicular Lines Acute Angle – any angle less than 90º Right Angle – a 90º angle Obtuse Angle - any angle larger than 90º Complementary Angles – angles that add up to 90º Supplementary Angles – angles that add up to 180º 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. Congruent Angles – Angles with equal measurement A ≅ B denotes that A is congruent to B. Transversal - a line that intersects a set of parallel lines t Vertical Angles Two angles that are opposite angles at intersecting lines. Vertical angles are congruent angles. t 1 2 3 4 1 4 2 3 Vertical Angles Find the measures of the missing angles t 125 ? 125 55 ? 55 Linear Pair Two adjacent angles that form a line. They are supplementary. (angle sum = 180) t 1+2=180 2+4=180 4+3=180 3+1=180 1 2 3 4 5 7 6 8 5+6=180 6+8=180 8+7=180 7+5=180 Supplementary Angles/ Linear Pair Find the measures of the missing angles t 108? 72 108 ? 180 - 72 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 Top Left Top Right 1 3 Bottom Left Top Left Bottom Left 2 4 Bottom Right 5 6 Top Right 7 8 Bottom Right 1 5 2 6 3 7 4 8 Corresponding Angles Find the measure of the missing angle t 145 35 ? 145 Alternate Interior Angles Two angles that lie between parallel lines on opposite sides of the transversal. These angles are congruent. t 1 2 3 4 5 6 7 8 3 6 4 5 Alternate Interior Angles Find the measure of the missing angle t 82 98 ?82 Alternate Exterior Angles Two angles that lie outside parallel lines on opposite sides of the transversal. They are congruent. t 1 2 3 4 5 6 7 8 2 7 1 8 Alternate Exterior Angles Find the measure of the missing angle t 120 60 ? 120 Same Side Interior Angles Two angles that lie between parallel lines on the same sides of the transversal. These angles are supplementary. t 1 2 3 4 3 +5 = 180 4 +6 = 180 5 6 7 8 *Also known as Consecutive Interior Angles Same Side Interior Angles Find the measure of the missing angle t 135 ?45 180 - 135 Same Side Exterior Angles Two angles that lie outside parallel lines on the same side of the transversal. These angles are supplementary. t 1 2 3 4 1 + 7 = 180 2 + 8 = 180 5 6 7 8 *Also known as Consecutive Exterior Angles Same Side Exterior Angles Find the measure of the missing angle t 135 ? 45 180 - 135 1,5 3,7 2,6 3,6 5,4 1,8 2,7 3,5 4,6 1,7 2,8 4,8 equivalent equivalent equivalent supplementary supplementary 112º 112º 68º 68º 112º 68º 68º 112º Closing What is a transversal? Name the types of equivalent angles. Name the types of supplementary angles.