Quiz (1 point)
Given that:
a ⋅ a = (b ⋅ b) + (c ⋅ c)
a = x
b = y
Prove that:
x ⋅ x = (y ⋅ y) + (c ⋅ c)
The following properties may be helpful:
if the following are true:
- x = a
- x ⋅ y = b
then a ⋅ y = b
if the following are true:
- a ⋅ b = c
- b = d
then a ⋅ d = c
if a = b, then a ⋅ c = b ⋅ c
if a = b, then c ⋅ a = c ⋅ b
if the following are true:
- a = b
- b = c
then a = c
if the following are true:
- a = b + c
- b = d
then a = d + c
Please write your proof in the table below. Each row should contain one claim. The last claim is the statement that you are trying to prove.