Proof: Similar Triangles Example 3

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	∠YPX and ∠XPZ are supplementary	if m∠YPZ = 180, then ∠YPX and ∠XPZ are supplementary (Supplementary Angles Theorem (Converse))
2	(m∠YPX) + (m∠XPZ) = 180	if ∠YPX and ∠XPZ are supplementary, then (m∠YPX) + (m∠XPZ) = 180 (Supplementary Angles Property)
3	m∠YPX = 90	if ∠XPY is a right angle, then m∠YPX = 90 (Right Angle is 90 Degres)
4	90 + (m∠XPZ) = 180	if (m∠YPX) + (m∠XPZ) = 180 and m∠YPX = 90, then 90 + (m∠XPZ) = 180 (Substitution 8)
5	m∠XPZ = 90	if 90 + (m∠XPZ) = 180, then m∠XPZ = 90 (Add Number to Both Sides 2)
6	m∠ZPX = 90	if m∠XPZ = 90, then m∠ZPX = 90 (Angle Symmetry Example 2)
7	∠ZPX is a right angle	if m∠ZPX = 90, then ∠ZPX is a right angle (Right Angle Property (Converse))
8	m∠ZXY = m∠ZPX	if ∠ZXY is a right angle and ∠ZPX is a right angle, then m∠ZXY = m∠ZPX (Right Angle Theorem)
9	m∠YZX = m∠PZX	if m∠YPZ = 180, then m∠YZX = m∠PZX (Collinear Angles Property C)
10	m∠YZX = m∠XZP	if m∠YZX = m∠PZX, then m∠YZX = m∠XZP (Angle Symmetry Example)
11	△ZXY ∼ △ZPX	if m∠YZX = m∠XZP and m∠ZXY = m∠ZPX, then △ZXY ∼ △ZPX (Similar Triangles Theorem)
12	△XYZ ∼ △PXZ	if △ZXY ∼ △ZPX, then △XYZ ∼ △PXZ (Similar Triangles)
13	△PXZ ∼ △XYZ	if △XYZ ∼ △PXZ, then △PXZ ∼ △XYZ (Symmetric Property of Similar Triangles)

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