Construct a two-column proof. Start with stating the given information.
Statements
Reasons
1.
a^2+b^2=c^2
1.
Given
2.
a^2+b^2-b^2=c^2-b^2
2.
Subtraction Property of Equality
3.
a^2=c^2-b^2
3.
Substitution Property of Equality
4.
a=±sqrt(c^2-b^2)
4.
Square Root Property of Equality
5.
a=sqrt(c^2-b^2)
5.
Length cannot be negative
Practice makes perfect
The right triangle shown below is given.
The Pythagorean Theorem states the length of c by the following equation.
Given: a^2+b^2=c^2
We will write a two-column proof to show that:
Prove: a=sqrt(c^2-b^2)
Let's start with stating the given to construct a two-column proof.
Given
a^2+b^2=c^2
Then, we will subtract b^2 from both side of the equation by the Subtraction Property of Equality.
Subtraction Property of Equality
a^2+b^2- b^2=c^2- b^2
Next, we will simplify the terms and rewrite the equation by using the Substitution Property of Equality.
Substitution Property of Equality
a^2=c^2-b^2
Now, we will take the square root of both sides of the equation by the Square Root Property of Equality.
Square Root Property of Equality
a=±sqrt(c^2-b^2)
As a last step, we will rewrite the equation since the length cannot be negative.
Length cannot be negative
a=sqrt(c^2-b^2)
Combining these steps, we will construct a two-column proof.
