Proof: Square Example 2

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	ABCD is a rhombus	if ABCD is a square, then ABCD is a rhombus (Square is Rhombus)
2	m∠BCA = m∠DCA	if ABCD is a rhombus, then m∠BCA = m∠DCA (Diagonal Bisects Rhombus 2)
3	m∠BCA = m∠ACD	if m∠BCA = m∠DCA, then m∠BCA = m∠ACD (Angle Symmetry Example)
4	ABCD is a rectangle	if ABCD is a square, then ABCD is a rectangle (Square Property)
5	∠BCD is a right angle	if ABCD is a rectangle, then ∠BCD is a right angle (Rectangle Right Angles 2)
6	m∠BCD = 90	if ∠BCD is a right angle, then m∠BCD = 90 (Right Angle Property)
7	quadrilateral ABCD is convex	if ABCD is a rectangle, then quadrilateral ABCD is convex (Rectangles Are Convex)
8	point A lies in interior of ∠BCD	if quadrilateral ABCD is convex, then point A lies in interior of ∠BCD (Convex Quadrilateral)
9	(m∠BCA) + (m∠ACD) = m∠BCD	if point A lies in interior of ∠BCD, then (m∠BCA) + (m∠ACD) = m∠BCD (Angle Addition Theorem 2)
10	(m∠BCA) + (m∠BCA) = m∠BCD	if (m∠BCA) + (m∠ACD) = m∠BCD and m∠BCA = m∠ACD, then (m∠BCA) + (m∠BCA) = m∠BCD (Substitute 2)
11	(m∠BCA) + (m∠BCA) = 90	if (m∠BCA) + (m∠BCA) = m∠BCD and m∠BCD = 90, then (m∠BCA) + (m∠BCA) = 90 (Transitive Property of Equality)
12	m∠BCA = 45	if (m∠BCA) + (m∠BCA) = 90, then m∠BCA = 45 (Reduce Addition 2)

Comments

Please log in to add comments