Geometry (Beta) / Chapter 2: Triangles / Equilateral Triangles

Proof: SSS

Let's prove the following theorem:

if distance AX = distance XB and M is the midpoint of line AB, then △AXM ≅ △BXM

A B X M

Proof:

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Given
1 distance AX = distance XB
2 M is the midpoint of line AB
Proof Table
# Claim Reason
1 distance XB = distance BX distance XB = distance BX
2 distance AX = distance BX if distance AX = distance XB and distance XB = distance BX, then distance AX = distance BX
3 distance XM = distance XM distance XM = distance XM
4 distance AM = distance MB if M is the midpoint of line AB, then distance AM = distance MB
5 distance MA = distance AM distance MA = distance AM
6 distance MA = distance MB if distance MA = distance AM and distance AM = distance MB, then distance MA = distance MB
7 △AXM ≅ △BXM if distance AX = distance BX and distance XM = distance XM and distance MA = distance MB, then △AXM ≅ △BXM
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