Recognition of Solids
73. The Oblique Sketch · True shapes, slanted sides, recognizable solids
Front and back faces stay congruent, and connecting edges remain parallel.
An oblique sketch is a quick freehand drawing that shows a 3D solid from a slanted angle. Front and back faces stay congruent (same shape and size); connecting edges are drawn parallel to give the illusion of depth.
What this lesson covers
Try to break it
Drag B to change the width, D to change the height, and H to stretch the depth. Notice how the front face keeps its true shape, and parallel lines stay parallel!
How you build it
Make an oblique sketch of a solid.
- Draw the front face of the solid as a rectangle.
- Draw the back face the same size, shifted diagonally.
- Join the top-left corners of the two faces.
- Join the top-right corners of the two faces.
- Join the bottom-right corners of the two faces.
- Join the bottom-left corners to complete the oblique sketch.
The proof, step by step
Prove that the oblique sketch keeps opposite faces congruent and connecting edges parallel.
- The front face is drawn in its true shape and size.
- The back face is congruent to the front face.
- Connecting edges are parallel to each other.
- Hidden edges are represented by dotted lines by convention.
Worked example
When drawing an oblique sketch of a cube, the front face is drawn as a ______.
In an oblique sketch, the front face is drawn in its true shape and size. For a cube, this is a square.
- Circle
- Square — correct
- Triangle
- Parallelogram