Last night during evening study, a student from the neighboring class came over to ask me about an interesting problem. The problem is as follows: In the diagram, let ∠BAC = α. Rotate triangle ABC around point C clockwise by α to obtain triangle A'B'C. Please draw triangle A'B'C using only an unmarked straightedge.Solution 1: First, rotate AC around point C clockwise by an angle of α to get A'C. Then, use A'C as a side to construct triangle A'CB' congruent to triangle ACB. This can be done using the ASA congruence criterion, as shown in the diagram below:Solution 2: After drawing A'C and ray CB' that forms an angle of α with CA' in Method 1, use the property of concurrent lines of the altitudes in isosceles triangle ACE to locate vertex B', as shown in the diagram below:
