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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercises 31 and 32, fill in the missing statements and reasons.

Given: M - N - P - Q on M Q ¯ Chapter 1.5, Problem 31E, In Exercises 31 and 32, fill in the missing statements and reasons. Given: M-N-P-Q on MQ Prove:
Prove: M N + N P + P Q = M Q
PROOF
Statements Reasons
1. ? 1. ?
2. M N + N Q = M Q 2. ?
3. N P + P Q = N Q 3. ?
4. 4. Substitution Property of Equality

To determine

To find:

The missing statements reasons.

Explanation

Given:

The given table is shown below.

PROOF
Statements Reasons
1. ? 1. ?
2. MN+NQ=MQ 2. ?
3. NP+PQ=NQ 3. ?
4. 4. Substitution Property of Equality

Properties:

1. According to Segment-Addition Postulate, if two points A, B are given on a line segment, then third point C lies on the line segment if and only if,

AC+CB=AB

2. According to Substitution Property of Equality, if A=B, then A can be substituted for B and B can be substituted for A in any equation.

Calculation:

The first statement of the proof should be the given information. So, the first statement is given as,

M-N-P-Q on MQ¯

Therefore, the first reason of the proof is Given.

Now, go from first statement to the second statement.

M-N-P-Q on MQ¯

Use Segment-Addition Postulate as points M,N, and Q are collinear and N lies between M and Q.

MN+NQ=MQ

Therefore, the second reason of the proof is Segment-Addition Postulate.

Now, go from first statement to third statement.

M-N-P-Q on MQ¯

Use Segment-Addition Postulate as points N,P, and Q are collinear and P lies between N and Q.

NP+PQ=NQ

Therefore, the third reason of the proof is Segment-Addition Postulate

To reach the final result, use second statement

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