Proof: Similar Triangles Example 2

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	m∠XYZ = m∠XYP	if m∠YPZ = 180, then m∠XYZ = m∠XYP (Collinear Angles Property 3 B)
2	m∠XYZ = m∠PYX	if m∠XYZ = m∠XYP, then m∠XYZ = m∠PYX (Angle Symmetry Example)
3	m∠ZXY = m∠XPY	if ∠ZXY is a right angle and ∠XPY is a right angle, then m∠ZXY = m∠XPY (Right Angle Theorem)
4	△XYZ ∼ △PYX	if m∠ZXY = m∠XPY and m∠XYZ = m∠PYX, then △XYZ ∼ △PYX (Similar Triangles Theorem)
5	△PYX ∼ △XYZ	if △XYZ ∼ △PYX, then △PYX ∼ △XYZ (Symmetric Property of Similar Triangles)

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