Level 105 Level 107
Level 106

Proof of Equilateral Triangle


9 words 0 ignored

Ready to learn       Ready to review

Ignore words

Check the boxes below to ignore/unignore words, then click save at the bottom. Ignored words will never appear in any learning session.

All None

Ignore?
Given
∆ABC is Equilateral
Prove
α∆ABC = x²√3/4
Step 1
Drop an altitude
Step 2
ISOBAM makes altitude an angle bisector
Step 3
Angle bisector makes the 60° angle into two 30° angles
Step 4
By definition, we now have a 30-60-90 triangle
Step 5
Because it is a 30-60-90, the height must be x√3/2 and the base must be ½x
Step 6
½b×h = x²√3/8
Step 7
Because there are two 30-60-90 triangles, we multiply by 2 to get the prove statement