Big Ideas Math Geometry, 2014
BI
Big Ideas Math Geometry, 2014 View details
5. Proving Statements about Segments and Angles
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Exercise 1 Page 100

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

Final Proof

Statement
Reason
1.
T is the midpoint of SU
1.
Given
2.
ST≅ TU
2.
Definition of midpoint
3.
ST=TU
3.
Definition of congruent segments
4.
7x=3x+20
4.
Substitution Property of Equality
5.
4x=20
5.
Subtraction Property of Equality
6.
x=5
6.
Division Property of Equality