Why is BE at a right angle to DG?

Drag the yellow points D and E. The sides AD and AE stay the same length.

These two squares help the purple line and the green line make a perfect corner!

Angle between BE and DG

90.0°

So, BE ⟂ DG

Step 1

AD = AE, so the triangle starts fairly balanced on both sides.

Step 2

Each square makes a right-angle turn. A square always has corners of 90°.

Step 3

When we turn the purple line by a quarter-turn, it matches the green line’s direction.

Purple line = BE

Green line = DG

Orange dashed line = turning copy of BE