# Finding isosceles triangles (performance task)

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Finding isosceles triangles

This task looks at some triangles in the coordinate plane and how to reason that these triangles

are isosceles. One way to do this is to calculate side lengths using the Pythagorean Theorem.

This method is not, however, always the most efficient. For the triangles given in parts (a) and

(b) two of the legs are obtained by moving along the grid lines, from one vertex, by the same

number of squares vertically and horizontally. Also, in parts (a) and (b), a line of reflective

symmetry is not hard to identify. So in these two cases there are alternative explanations and

the teacher may wish to emphasize this. For part (c), it is not easy to see that this triangle is

isosceles without the Pythagorean Theorem. The teacher may wish to ask students to explain

why the triangles in (a) and (b) are isosceles without using the Pythagorean Theorem if this does

not come up in student work.

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