1. Angles
GM1.1 Core Plenary
You know the values of angles x and y.
Write down, with reasons, expressions for the values of as many other angles as you can.
How many more angles can you find if CB is parallel to JF?
What happens if CJ and FH are also parallel? x y B C E G A D F H I J K
Preamble Pupils need to understand the importance of giving reasons for the steps in their working. It may be convenient to have a batch of reasons prepared beforehand – perhaps a whole-class activity using a projector or interactive whiteboard. The task illustrates the importance of using some form of unambiguous angle identification.
Possible content Angles properties of triangles and transected parallel lines.
Resources None.
Solution/Notes Many angles can be determined; these are some examples. EGH = 180° – x – y (angle sum of AGH is 180°) EGF = x + y (exterior angle of AGH is the sum of the interior opposite angles) FEG = 180° – x – 2y (angle sum of EFG is 180°)
DEJ = FEG = 180° – x − 2y (vertically opposite angles) With CB parallel to JF CBD = DEJ = 180 – x − 2y (alternate angles)
With CB parallel to JF, and CJ parallel to FH GFE = DJE = y (alternate angles) BCD = DJE = y (alternate angles)
Original Material © Cambridge University Press 2009
Original Material © Cambridge University Press 2009