Teaching triangle height: a same-base, same-area board sequence (developer resource)

[u/readhub]

I'm Chen, the developer of Whiteboard by Endless AI. For Saturday resource sharing, here is a short board sequence for teachers introducing perpendicular height. It also works on graph paper; the activity doesn't require my app.

1. Draw a base from A(0,0) to B(4,0). Use C(2,3) as the third vertex. Before adding measurements, ask students which segment they would need to measure to find the area.

2. Beside it, draw a second triangle with the same A and B but with C at (6,3). Ask students to predict whether its area is larger, smaller, or equal, and explain what they are comparing. Leave the two predictions visible.

3. Add the horizontal guide y=3 and perpendicular heights. In the second triangle, extend the base line to show why the height lands outside the triangle. Both areas are 4 x 3 / 2 = 6 square units, despite different sloping sides.

For an exit prompt, put C at (6,4): what changed, and why is the new area 8 rather than 6? This separates 'move sideways' from 'change the height.'

On Whiteboard for iPad, you can sketch this with the coordinate-system and line tools, use a different color for the heights, and export the annotated page as a PDF. These are manually drawn comparisons, not a constrained draggable geometry construction. The app is free to download with optional paid features. Downloads and illustrated iOS Help: https://endlessai.org/

For teachers who use this comparison, would you reveal the outside altitude immediately, or first ask students to draw their own proposed height?

[u/watchfuldominion4]

The sideways slide trick is a clean way to separate base and height, wish I'd seen this when I first taught that unit