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MAT402

Practice exam

Classical geometries

1.) (Circle and straightedge construction) Given a line segment , give a step-by-step construction (including a picture for each step) of a right-angled triangle with hypotenuse and ∠BAC = 30◦ . You may use euclidea.xyz or include freehand drawings.

2.) Assume that is an isometry and that ∆ABC is a triangle such that f(A) = B, f(B) = A and f(C) = C. Prove that f is a reflection.

3.) Let Find the equations for two hyperbolic lines  Your solutions should include detailed computations and justifications.