Proof: Perpendicular Bisector Theorem

Let's prove the following theorem:

if SM ⊥ MY and M is the midpoint of line XY, then distance SX = distance SY

S M X Y

Proof:

View as a tree | View dependent proofs | Try proving it

Given
1 SM ⊥ MY
2 M is the midpoint of line XY
Proof Table
# Claim Reason
1 m∠XMY = 180 if M is the midpoint of line XY, then m∠XMY = 180
2 ∠SMY is a right angle if SM ⊥ MY, then ∠SMY is a right angle
3 m∠SMY = 90 if ∠SMY is a right angle, then m∠SMY = 90
4 ∠XMS and ∠SMY are supplementary if m∠XMY = 180, then ∠XMS and ∠SMY are supplementary
5 (m∠XMS) + (m∠SMY) = 180 if ∠XMS and ∠SMY are supplementary, then (m∠XMS) + (m∠SMY) = 180
6 (m∠XMS) + 90 = 180 if (m∠XMS) + (m∠SMY) = 180 and m∠SMY = 90, then (m∠XMS) + 90 = 180
7 m∠XMS = 90 if (m∠XMS) + 90 = 180, then m∠XMS = 90
8 m∠SMY = m∠XMS if m∠SMY = 90 and m∠XMS = 90, then m∠SMY = m∠XMS
9 m∠XMS = m∠YMS if m∠SMY = m∠XMS, then m∠XMS = m∠YMS
10 distance XM = distance MY if M is the midpoint of line XY, then distance XM = distance MY
11 distance XM = distance YM if distance XM = distance MY, then distance XM = distance YM
12 distance MS = distance MS distance MS = distance MS
13 △XMS ≅ △YMS if distance XM = distance YM and m∠XMS = m∠YMS and distance MS = distance MS, then △XMS ≅ △YMS
14 distance SX = distance SY if △XMS ≅ △YMS, then distance SX = distance SY

Comments

Please log in to add comments