Question

Draw a triangle and a line m such that $R_m$ maps the triangle to itself. What kind of triangle did you use?

Short answer

An equilateral triangle with any of its median as line of reflection.

Step-by-step solution

Step 1. Given Information.

After reflection the image is same as previous.

Step 2. Explanation.

In an equilateral triangle all the angles are same.

So, when a median drawn, all the corresponding angle are equal.

As median divides the side in two equal parts the corresponding sides are also equal.

Step 3. Conclusion.

Hence, an equilateral triangle with any of its median as line of reflection.