Sections 2.1 – 2.3: Dangerous Definitions Directions: The first two questions of your 2.1 – 2.3 Quiz will be vocabulary words that you have to write out the definitions for. Each definition will count for 3 points (which is 15%) of your quiz grade. Definitions are dangerous – if you skip just one word, or change the wording a little, you sometimes wind up saying something totally different and wrong…. or something that we can’t clearly understand (mathematically). As practice, try to find the flaw with each of the following (wrong) “definitions”. The following wrong definitions came from kids’ past quizzes; these each received 0 points. Opposite Rays (Correct Definition): If C is between A and B, the and are opposite rays •
First, draw an of example of opposite rays here: Draw a picture that fits this WRONG “definition”, BUT does NOT show a true example of opposite rays INCORRECT, KID-­INVENTED “DEFINITION” OF TERM: Opposite Rays (Incorrect) – Two rays are opposite rays if they are on the same line but point in opposite directions Opposite Rays (Incorrect) – Two rays that have the same initial point but point in opposite directions are opposite rays Opposite Rays (Incorrect) -­ and are opposite rays ____ and ____ are NOT really opposite rays ____ and ____ are NOT really opposite rays ____ and ____ are NOT really opposite rays Segment Addition Postulate (Correct Definition) – If B is between A and C, then AB + BC = AC. •
Draw an example where you could use the Segment Addition Postulate (include sample lengths in pic): EXPLANATION FOR WHY IT’S AN INCORRECT “DEFINITION” INCORRECT, KID-­INVENTED “DEFINITION” OF TERM: Segment Addition Post. (Incorrect) – If B is between A and C, then Segment Addition Post. (Incorrect) – AB + BC = AC Explain the error: Draw a segment, with sample lengths, where AB + BC AC Segment Addition Post. (Incorrect) -­ If B is between , then AB + BC = AC. Segment Addition Post. (Incorrect) –If B is the midpoint of , then The word “between” is used incorrectly here. We can only use the word “between” when talking about _________________. Explain the error: Angle Addition Postulate (Correct Definition) – If C is in the interior of AOD, then m AOC + m COD = m
• Draw an example where you could use the Angle Addition Postulate (include sample angle measures): AOD. EXPLANATION FOR WHY IT’S AN INCORRECT “DEFINITION” INCORRECT, KID-­INVENTED “DEFINITION” OF TERM: Angle Addition Postulate (Incorrect) – If C is in the interior of AOD, then AOC + COD = AOD. Angle Addition Postulate (Incorrect) – m AOC + m COD = m AOD. Explain the error: Angle Addition Postulate (Incorrect) -­ If m
ERROR: The word “interior of angle” is used incorrectly here. We can only say ______________ (not rays) are in the “interior of an angle”. ERROR: The word “between” is used incorrectly here. We can only use the phrase “between” with _____________________ (not rays). Explain the error: Angle Addition Postulate (Incorrect) – If m
is in the interior of AOD, then AOC + m COD = m AOD is between AOD, then AOC + m COD = m AOD. Angle Addition Postulate (Incorrect) -­ If divides AOD into two congruent angles, then m AOC + m COD = m
AOD. Draw an angle, with sample measures, where m
AOC + m COD m AOD Segment bisector (Correct Definition): a segment, ray, line, or plane that intersects a segment at its midpoint. *Draw a segment that is a segment bisector *Draw a line that is a segment bisector * Draw a ray that is a segment bisector * Draw a plane that is a segment bisector EXPLANATION ABOUT WHY IT’S INCORRECT, KID-­INVENTED “DEFINITION” OF TERM: A WRONG “DEFINITION” Segment Bisector (Incorrect) – A segment, ray, or line that intersects a segment at the segment’s midpoint. Segment Bisector (Incorrect) – A segment, ray, line, plane, or point that intersects a segment at the segment’s midpoint. Explain the error: Segment Bisector (Incorrect) – A segment, ray, line, or plane that intersects a line at its midpoint Explain the error: Why isn’t a POINT that intersects a segment at its midpoint called a “segment bisector”? Errors of Omission: Each of the following “definitions” is missing a key word or words. Illustration of why the “definition” is wrong and/or a list of missing words INCORRECT, KID-­INVENTED “DEFINITION” OF TERM: from (wrong) “definition” Draw a
p
icture that fits this description but is NOT truly an angle: Angle (Incorrect) – An angle consists of two different rays. The rays are the sides of the angle and the initial point is the vertex of the angle. Obtuse Angle (Incorrect) – An angle with a measure greater than 90o Exterior of an Angle (Incorrect) – Every nonstraight angle has an exterior. A point D is in the exterior of A if is not in the interior of the angle. Collinear (Incorrect)– points that lie on the same line Collinear (Incorrect)– point, ray, segment, or line that lies on the same line Adjacent Angles (Incorrect) – two angles are adjacent if they share a common side and vertex Midpoint (Incorrect) -­ the point that divides the segment into two segments Angle Bisector (Incorrect) – a point that divides an angle into two angles Missing word(s): Draw a picture that fits this description but is NOT truly an obtuse angle: Missing word(s): Draw an angle. Then label a point that fits this description but is NOT truly in the “exterior of the angle” that you drew. ______ is NOT in the exterior of _____ Missing word(s): Draw a picture that does NOT follow this description but DOES show collinear objects (besides points): _____ and _____ are also collinear in this pic Missing word(s): Letters that need to be added: Why does this matter? Draw a picture that fits this description but does NOT truly show adjacent angles: _______ and ______ are NOT adjacent angles Missing word(s) Draw a picture that fits this description but does NOT truly show a midpoint. _____ is NOT a midpoint in this picture. Missing word(s): Which word is wrong? What should it say instead?