1. **Problem Statement:** Given two projections of triangle ABC, we need to draw the true size and real shape of triangle ABC. 2. **Understanding the Problem:** The two projections represent different views of the same triangle. The goal is to reconstruct the actual triangle in true size and shape from these projections. 3. **Key Concept:** The true size and shape of a triangle can be found by using the projections and applying geometric principles such as rotation, translation, and scaling to align the projections correctly. 4. **Step-by-step Solution:** 1. Identify corresponding points in both projections: $A, B, C$ in the first and $A', B', C'$ in the second. 2. Note the line $X$ which acts as a reference or ground line for aligning the projections. 3. Use the points $O$ and $o$ on line $X$ to establish a common baseline. 4. Rotate and translate one projection so that the baseline points $O$ and $o$ coincide with the other projection's baseline. 5. After alignment, measure distances between points $A, B, C$ and $A', B', C'$ to find the true lengths. 6. Using these true lengths, reconstruct triangle $ABC$ on a plane to get the true size and shape. 5. **Formula/Rule:** The true length $L$ between two points in space can be found by combining their projections using the Pythagorean theorem if projections are perpendicular: $$L = \sqrt{L_1^2 + L_2^2}$$ where $L_1$ and $L_2$ are lengths from the two projections. 6. **Explanation:** By combining the two perpendicular projections, we recover the actual distances between points, allowing us to draw the triangle in its true size and shape. 7. **Final Answer:** The true size and shape of triangle $ABC$ is obtained by reconstructing it using the combined lengths from the two projections after aligning them along the reference line $X$.