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Length of a Line in Projection
Last updated at February 26, 2026 by Teachoo
Class 8 (Ganita Prakash - 1, 2 & Old NCERT)
Chapter 4 Class 8 - Exploring Some Geometric Themes (Ganita Prakash II
- Fractals
- Sierpinski Carpet
- Sierpinski Gasket
- Figure it out - Page 72
- Koch Snowflake
- Fractals in Art
- Imagining Solids
- Solid Shapes
- Net of a Cube
- Net of other Figures
- Shortest Paths on a Cube
-
Projections
- Top view, Front View, Side view
- Shadows as Projections
- Figure it out - Page 95-97
- Isometric Projections
- Drawing on Isometric Grids
- Figure it out - Page 100, 101
Transcript
Length of a line in ProjectionWhen we projected our line, we noticed that length is different depending on the angle Let l be the actual length of the line & p be the length of its projection. Draw AE ⊥ BC. Since CD is a projection AD ⊥ Plane & BC ⊥ Plane Since all 4 angles are 90° AECD is a rectangle Thus, AE = DC = p And, ∠AEB = 90°. In Right triangle ∆ AEB Using Pythagoras Theorem AB2 = AE2 + BE2 l2 = p2 + BE2 Thus, p is smaller than or equal to l Let’s look at some examples ExamplesWe notice different values of p depending on the tilt
