Notice that there is some information in the diagram that you will need.
See solution.
Practice makes perfect
We are given a two-column proof with several blanks and are asked to fill in those blank spaces. Let's begin by looking at the given information and the desired outcome of the proof.
Given:& T is the midpoint of $SU$
Prove:& x=5
Now, let's take a look at the statement and the reasons that need to be completed one at a time.
Blank 1
In the first row the reason is missing. Examining the statement, we see that it states the given information.
&1. T is the midpoint of SU
&1. Given
Blank 4
The fourth row shows an equation and a missing reason. From the previous statements in our two-column proof, we know that ST and TU are congruent segments. Examining the diagram, we also know that ST=7x and TU=3x+20. Therefore, to write the statement in 4 we have to use the Substitution Property of Equality.
&4. 7x=3x+20
&4. Substitution Property of Equality
Blank 5
Using the Subtraction Property of Equality, we can subtract any number or variable from both sides of an equation without breaking the equality. Since our goal is to solve the equation, we need to isolate the variable on one side of the equation. Therefore, we have to subtract 3x from both sides of the equation.
7x - 3x&= 3x+20 - 3x
4x&= 20
We can fill out the statement in the fifth row.
&5. 4x=20
&5. Subtraction Property of Equality
Blank 6
To fill in the missing reason, we have to compare the statements in the fifth and sixth rows.
&5. 4x=20
&6. x=5
To go from 5 to 6, we have to isolate x on the left-hand side. Because x is multiplied by 4, we have to divide by 4 to isolate x. The reason is therefore the Division Property of Equality.
&6. x=5
&6. Division Property of Equality
