Proof: Diagonal Bisects Rhombus 2

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	△PWX ≅ △PYZ	if WXYZ is a rhombus and m∠WPY = 180 and m∠XPZ = 180, then △PWX ≅ △PYZ (Triangles Inside Rhombus)
2	distance XP = distance ZP	if △PWX ≅ △PYZ, then distance XP = distance ZP (Congruent Triangles Property 9)
3	distance PY = distance PY	distance PY = distance PY (Reflexive Property of Equality)
4	distance XY = distance YZ	if WXYZ is a rhombus, then distance XY = distance YZ (Sides of Rhombus Congruent 4)
5	distance YX = distance YZ	if distance XY = distance YZ, then distance YX = distance YZ (Distance Property 1)
6	△PYX ≅ △PYZ	if distance PY = distance PY and distance YX = distance YZ and distance XP = distance ZP, then △PYX ≅ △PYZ (SSS Property)
7	m∠PYX = m∠PYZ	if △PYX ≅ △PYZ, then m∠PYX = m∠PYZ (Congruent Triangles Property 4)
8	m∠XYP = m∠ZYP	if m∠PYX = m∠PYZ, then m∠XYP = m∠ZYP (Angle Symmetry 2)
9	m∠XYW = m∠ZYW	if m∠WPY = 180 and m∠XYP = m∠ZYP, then m∠XYW = m∠ZYW (Equal Angles 2)

Comments

Please log in to add comments