Question

A student claimed that reflect a triangle in a line, translating a triangle , rotating a triangle, and reflecting it in a point result in an image that is congruent to the original( pre-image) triangle. explain why they are correct.

Answer 1

If we reflect a triangle in a line, translate a triangle, rotate a triangle, and reflect it in a point result in an image that will be congruent to the original( pre-image) triangle.

This is a problem from triangular geometry. We can solve this problem by following a few steps.

Here a triangle ABC is given and the triangle is at first reflected and then translated, thereafter it rotates and is later reflected.

After all, these processes the value of ∠A, ∠B, and ∠ C remains the same as usual concerning ∠A''', ∠B''', ∠ and C'', as they just changes coordinates not geometric structures.

After all these processes the length of the triangle AB, AC, BD, and A'''B''', B'''C''', C'''A''' remains the same as usual.

∵ We can conclude that ΔABC ≅ ΔA'''B'''C'''

( As AB = A'''B''', BC = B'''C''', ∠ABC = ∠ A'''B'''C''' )

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