Proof: Acute Angles of Right Triange Comlementary

Let's prove the following theorem:

if △XYZ is a right triangle, then (m∠YZX) + (m∠ZXY) = 90

Proof:

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

Given

1	△XYZ is a right triangle

Proof Table

#	Claim	Reason
1	m∠XYZ = 90	if △XYZ is a right triangle, then m∠XYZ = 90 (Right Triangle Property)
2	((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180	((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180 (triangles_sum_to_180)
3	(90 + (m∠YZX)) + (m∠ZXY) = 180	if ((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180 and m∠XYZ = 90, then (90 + (m∠YZX)) + (m∠ZXY) = 180 (Substitute First Term)
4	(m∠YZX) + (m∠ZXY) = 180 + (90 ⋅ (-1))	if (90 + (m∠YZX)) + (m∠ZXY) = 180, then (m∠YZX) + (m∠ZXY) = 180 + (90 ⋅ (-1)) (Add Term to Both Sides 4)
5	(m∠YZX) + (m∠ZXY) = 90	if (m∠YZX) + (m∠ZXY) = 180 + (90 ⋅ (-1)), then (m∠YZX) + (m∠ZXY) = 90 (Subtraction Example 2)

Comments

Please log in to add comments