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Transcript
Angle › Formed by two rays with the same endpoint Vertex › The name for the common endpoint Sides › The rays that make up the angle An angle can be named in a few different ways: With an angle symbol and the vertex óA Or using three points The vertex must always be in the middle! › óBAC or › óCAB Or with a number on the inside of the angle › ó4 Interior contains all the points between the two sides Exterior contains all the points outside the angle Between 0 and 90 degrees xO Exactly 90O Between 90 and 180 degrees xO Exactly 180o xO Draw an angle on one side of paddy paper Fold the paper in half Trace the angle on the other side of the paper You should see two angles Answer Question 1 on the work sheet Cut out one of the angles leaving the other on the paper Cut the separate angle into two different angles through the vertex You should now have one angle on paper and one cut into two pieces Place the cut angle onto the original angle any way as long as the vertex lines up Answer question 2 Notice how the two pieces add up to the one angle Remember how two pieces of a line add up to the whole If point B is in the interior of óAOC, then óAOB + óBOC = óAOC If óROT = 155O, what are the measures of angles ROS and SOT? Remember: (4x - 20)O (3x + 14)O Plug in each piece and make it equal the total (4x - 20)O (3x + 14)O Combine like terms Add 6 to both sides Divide by 7 If óROT = 155O, what are the measures of angles ROS and SOT? So if x = 23, plug it into 4x – 20 to find óROS (4x - 20)O (3x + 14)O If óROT = 155O, what are the measures of angles ROS and SOT? So if x = 23, plug it into 3x + 14 to find óSOT 72O (3x + 14)O If óROT = 155O, what are the measures of angles ROS and SOT? Do your answers make sense? 72O 83O If móAMC = 140, what is x? Find móAMB. (3x + 17)O (5x – 45)O Two or more angles that have the same measure 40O 40O Take one piece of Patty Paper (tracing paper) Draw two straight and intersecting lines The angles don’t matter except they should not be 90 degrees Label the intersection point E Put a point on each ray A, B, C, and D Fold the paper at the point E so that ray EA and ray ED line up on top of each other Answer questions 1 and 2 Fold the paper at the point E so that ray EA and ray EB line up on top of each other Answer questions 3 and 4 Mark the pairs of congruent angles Notice how the vertical angles (across from each other) are congruent Two angles whose sides are opposite rays Think the opposite sides of an x They are congruent Two coplanar angles with a common side, a common vertex, and no common interior points Angles AMB and BMC are adjacent Angles AMB and CMC are not! Angles AMB and CMC are not! › They don’t have a common side Angles AMC and BMC are not! › They share common point between B and C Two angles whose measures have a sum of 90 degrees. Each angle is called the complement of the other 50O Two angles whose measures have a sum of 180 degrees Each angle is called the supplement of each other 50O If two angles form a linear pair, then they are supplementary 120O 60O A ray that cuts an angle into two congruent angles