Alternate Interior Angles Theorem

if m∠WSX = 180 and m∠YTZ = 180 and m∠WST = m∠STZ, then WX || YZ

Given(s)

• m∠WSX = 180

• m∠YTZ = 180

• m∠WST = m∠STZ

Proof Table

#	Claim	Reason
1	m∠WPX = 180	if line WX intersects line YZ at point P, then m∠WPX = 180 (Intersecting Lines Property)
2	m∠WSP = 180	if m∠WSX = 180 and m∠WPX = 180, then m∠WSP = 180 (Collinear Points Property 3)
3	m∠YPZ = 180	if line WX intersects line YZ at point P, then m∠YPZ = 180 (Intersecting Lines Property 2)
4	m∠TPZ = 180	if m∠YTZ = 180 and m∠YPZ = 180, then m∠TPZ = 180 (Collinear Points Property 4)
5	m∠WST > m∠STP	if m∠WSP = 180, then m∠WST > m∠STP (Exterior Angle B)
6	m∠STP = m∠STZ	if m∠TPZ = 180, then m∠STP = m∠STZ (Collinear Angles Property 3 C)
7	m∠WST > m∠STZ	if m∠WST > m∠STP and m∠STP = m∠STZ, then m∠WST > m∠STZ (Transitive Property of Inequality 3)

Conclusion

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