Maths Olympiad Prep

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Geometry Difficulty 2.6 Junior Find the answer Canada

Triangle TT is reflected once.


Hide/Reveal Description of Triangles

Triangle A> Starting at the vertex of the 90 degree angle, the shorter side goes up and the longer side goes left.
Triangle B> Starting at the vertex of the 90 degree angle, the shorter side goes up and the longer side goes left.
Triangle C> Starting at the vertex of the 90 degree angle, the shorter side goes up and the longer side goes right.
Triangle D> Starting at the vertex of the 90 degree angle, the shorter side goes down and the longer side goes left.
Triangle E> Starting at the vertex of the 90 degree angle, the shorter side goes down and the longer side goes left.

Which of the following triangles cannot be this reflection of triangle TT?

Pick one

Solution

Each of the following four diagrams shows the image of triangle TT after its reflection in the dotted line.

[[IMAGE0]]

Thus, each of the triangles labelled A,B,D,A, B, D, and EE is a single reflection of triangle TT in some line.

The triangle labelled CC is the only triangle that cannot be a reflection of triangle TT.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.