Lesson 1 · Lines and Angles

Pairs of Angles Presentation

MathematicsSubject
14 minEstimated read
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Unit 1 · Lines and Angles

Pairs of Angles

Mathematics · Grade 7

Three Facts, Nothing Else

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A straight line is 180°. Always true, no conditions

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A full turn is 360°. Always true, no conditions

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Parallel lines slide an angle along unchanged. Only if truly parallel

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Every name in this topic is one of these three with a label on it

Vertically Opposite, Proved in Four Lines

1Two lines cross. Label the four angles a, b, c, d going round
2a and b lie on one straight line, so a + b = 180
3b and c lie on the other straight line, so b + c = 180
4Both equal 180, so a + b = b + c. Take b off both sides
5a = c. Nothing was measured and no lines had to be parallel

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Presenter notes: Open by writing all seven names on the board in a long column: complementary, supplementary, adjacent, linear pair, vertically opposite, corresponding, alternate, co-interior. Let the class look at it and feel how much there is to learn. Then say that by the end of the lesson that column will have collapsed into three lines, and that nobody is going to memorise the list. This framing matters, because a student who believes there are eight separate things to learn will study it as vocabulary, and a student who believes there are three will study it as reasoning.