Respuesta :
The respective reasons, chosen from the given word bank, for each of the statements in the proof are given as follows:
1. Given
2. Definition of Congruence
3. Segment Addition Postulate
4. Substitution Property
5. Substitution Property
6. Transitive Property
7. Definition of Congruence
Given data: [tex]\overline{PQ}=\overline{TQ}[/tex], [tex]\overline{UQ}=\overline{QS}[/tex]
To provide: The reasons for each statement leading to the proof of [tex]\overline{PS}=\overline{TU}[/tex]
The given word bank is:
- Transitive Property
- Substitution Property
- Definition of Congruence
- Substitution Property
- Definition of Congruence
- Segment Addition Postulate
- Given
The explanations for each word in the word bank is as follows:
Transitive Property: If [tex]x=y[/tex] and [tex]y=z[/tex], then [tex]x=z[/tex]
Substitution Property: If two quantities are equal, then one quantity can be replaced in a statement involving the other quantity.
Definition of Congruence: Two line segments are defined to be congruent if their lengths are equal.
Segment Addition Postulate: Adding two line segments, if they are part of the same line, results in the line segment containing both the line segments.
Given: Listing the given conditions in any mathematical problem.
Now, the statements leading up to the required proof and their reasons are given as follows:
Statement 1. [tex]\overline{PQ}=\overline{TQ}[/tex], [tex]\overline{UQ}=\overline{QS}[/tex]
Reason 1. Given
Explanation: Listing the given conditions
Statement 2. [tex]PQ=TQ[/tex], [tex]UQ=QS[/tex]
Reason 2. Definition of Congruence
Explanation: Statement 2 directly follows from Statement 1 by the definition of congruence of line segments
Statement 3. [tex]PQ+QS=PS[/tex], [tex]TQ+QU=TU[/tex]
Reason 3. Segment Addition Postulate
Explanation: Two line segments are added to get a line segment containing both segments
Statement 4. [tex]TQ+QS=PS[/tex]
Reason 4. Substitution Property
Explanation: The first part of Statement 2. is substituted into the first part of Statement 3
Statement 5. [tex]TQ+QS=TU[/tex]
Reason 5. Substitution Property
Explanation: The second part of Statement 2 is substituted into the second part of Statement 3
Statement 6. [tex]PS=TU[/tex]
Reason 6. Transitive Property
Explanation: The Statements 4 and 5 constitute the condition and Statement 6 constitutes the result of applying transitive property
Statement 7. [tex]\overline{PS}=\overline{TU}[/tex]
Reason 7. Definition of Congruence
Explanation: The Statement 6 implies the equality of two line segments. Applying the definition of congruence, it implies the congruence of those line segments
These are the respective reasons, chosen from the given word bank, for each of the statements in the proof.
Learn more about giving reasons for statements in proofs here:
https://brainly.com/question/11120727
