Find answers to your questions faster and easier with IDNLearn.com. Our platform provides accurate, detailed responses to help you navigate any topic with ease.
Sagot :
To complete the proof, let's fill in the missing statements and reasons in the table.
Given: [tex]\(M-N-P-Q\)[/tex] on [tex]\(\overline{MQ}\)[/tex]
Prove: [tex]\(MN + NP + PQ = MQ\)[/tex]
[tex]\[ \begin{array}{|c|c|} \hline \text{Statements} & \text{Reasons} \\ \hline 1. M - N - P - Q \text{ on } \overline{MQ} & 1. \text{Given} \\ 2. MN + NQ = MQ & 2. \text{By the definition of a line segment} \\ 3. NP + PQ = NQ & 3. \text{By the definition of a line segment} \\ 4. MN + NP + PQ = MQ & 4. \text{Substitution Property of Equality} \\ \hline \end{array} \][/tex]
Detailed Explanation:
1. Statement 1: Given
[tex]\(M-N-P-Q\)[/tex] on [tex]\(\overline{MQ}\)[/tex] means that points M, N, P, and Q are collinear on the line segment from [tex]\(M\)[/tex] to [tex]\(Q\)[/tex].
2. Statement 2: [tex]\(MN + NQ = MQ\)[/tex]
Reason: By the definition of a line segment, the total distance [tex]\(MQ\)[/tex] can be expressed as the sum of the distances from [tex]\(M\)[/tex] to [tex]\(N\)[/tex] and from [tex]\(N\)[/tex] to [tex]\(Q\)[/tex]. This is because [tex]\(N\)[/tex] is between [tex]\(M\)[/tex] and [tex]\(Q\)[/tex].
3. Statement 3: [tex]\(NP + PQ = NQ\)[/tex]
Reason: Similarly, the distance [tex]\(NQ\)[/tex] can be expressed as the sum of the distances from [tex]\(N\)[/tex] to [tex]\(P\)[/tex] and from [tex]\(P\)[/tex] to [tex]\(Q\)[/tex]. This is because [tex]\(P\)[/tex] is between [tex]\(N\)[/tex] and [tex]\(Q\)[/tex].
4. Statement 4: [tex]\(MN + NP + PQ = MQ\)[/tex]
Reason: Substitution Property of Equality. Using statement 3, substitute [tex]\(NQ\)[/tex] in statement 2 with [tex]\(NP + PQ\)[/tex]:
[tex]\[ MN + (NP + PQ) = MQ \][/tex]
Which simplifies to:
[tex]\[ MN + NP + PQ = MQ \][/tex]
Thus, we have shown using the definitions of line segments and the substitution property of equality that [tex]\(MN + NP + PQ = MQ\)[/tex].
Given: [tex]\(M-N-P-Q\)[/tex] on [tex]\(\overline{MQ}\)[/tex]
Prove: [tex]\(MN + NP + PQ = MQ\)[/tex]
[tex]\[ \begin{array}{|c|c|} \hline \text{Statements} & \text{Reasons} \\ \hline 1. M - N - P - Q \text{ on } \overline{MQ} & 1. \text{Given} \\ 2. MN + NQ = MQ & 2. \text{By the definition of a line segment} \\ 3. NP + PQ = NQ & 3. \text{By the definition of a line segment} \\ 4. MN + NP + PQ = MQ & 4. \text{Substitution Property of Equality} \\ \hline \end{array} \][/tex]
Detailed Explanation:
1. Statement 1: Given
[tex]\(M-N-P-Q\)[/tex] on [tex]\(\overline{MQ}\)[/tex] means that points M, N, P, and Q are collinear on the line segment from [tex]\(M\)[/tex] to [tex]\(Q\)[/tex].
2. Statement 2: [tex]\(MN + NQ = MQ\)[/tex]
Reason: By the definition of a line segment, the total distance [tex]\(MQ\)[/tex] can be expressed as the sum of the distances from [tex]\(M\)[/tex] to [tex]\(N\)[/tex] and from [tex]\(N\)[/tex] to [tex]\(Q\)[/tex]. This is because [tex]\(N\)[/tex] is between [tex]\(M\)[/tex] and [tex]\(Q\)[/tex].
3. Statement 3: [tex]\(NP + PQ = NQ\)[/tex]
Reason: Similarly, the distance [tex]\(NQ\)[/tex] can be expressed as the sum of the distances from [tex]\(N\)[/tex] to [tex]\(P\)[/tex] and from [tex]\(P\)[/tex] to [tex]\(Q\)[/tex]. This is because [tex]\(P\)[/tex] is between [tex]\(N\)[/tex] and [tex]\(Q\)[/tex].
4. Statement 4: [tex]\(MN + NP + PQ = MQ\)[/tex]
Reason: Substitution Property of Equality. Using statement 3, substitute [tex]\(NQ\)[/tex] in statement 2 with [tex]\(NP + PQ\)[/tex]:
[tex]\[ MN + (NP + PQ) = MQ \][/tex]
Which simplifies to:
[tex]\[ MN + NP + PQ = MQ \][/tex]
Thus, we have shown using the definitions of line segments and the substitution property of equality that [tex]\(MN + NP + PQ = MQ\)[/tex].
I got it wrong because I went with different answers trust me it’s -2 1/4 or D
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.
