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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 1.CT, Problem 20CT
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Elementary Geometry for College St...

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

Solutions

Chapter
Section
Problem 1CT
Problem 2CT
Problem 3CT
Problem 4CT
Problem 5CT
Problem 6CT
Problem 7CT
Problem 8CT
Problem 9CT
Problem 10CT
Problem 11CT
Problem 12CT
Problem 13CT
Problem 14CT
Problem 15CT
Problem 16CT
Problem 17CT
Problem 18CT
Problem 19CT
Problem 20CT
Problem 21CT
Problem 22CT
Problem 23CT
BuyFindarrow_forward

Elementary Geometry for College St...

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

In exercises 20 to 22, complete the missing statements/ reasons for each proof.

Given: M − N − P − Q on M Q ¯
Prove: M N + N P + P Q = M Q

Chapter 1.CT, Problem 20CT, In exercises 20 to 22, complete the missing statements/ reasons for each proof. Given: MNPQ on MQ

PROOF
Statements Reasons
1. M − N − P − Q on M Q ¯ 1. ______________________
2. M N + N Q = M Q 2. ______________________
3. N P + P Q = N Q 3. ______________________
4. M N + N P + P Q = M Q 4. ______________________

To determine

To find:

The missing statements/reasons for the each proof.

Explanation

Given:

The given figure is,

The given table is shown below.

PROOF
Statements Reasons
1. M−N−P−Q on MQ¯ 1. ______________________
2. MN+NQ=MQ 2. ______________________
3. NP+PQ=NQ 3. ______________________
4. MN+NP+PQ=MQ 4. ______________________

Properties:

a. The segment addition postulate states that if 3 points A, B, and C are collinear and B is between A and C, then AB+BC=AC.

b. According to Substitution Property, if x=y, then x can be substituted for y and y can be substituted for x in any equation.

Calculation:

The first statement of the proof is given. That is.

M−N−P−Q on MQ¯

The second statement of the proof is based on segment addition postulate. So, use Segment addition postulate in the given diagram.

MN+NQ=MQ…(1)

The third reason is based on segment addition postulate. So, use Segment addition postulate in the given diagram.

NP+PQ=NQ…(2)

The fourth statement of the proof is based on substitution property.

MN+NQ=MQNQ=MQ−MN

Substitute MQ−MN for NQ in equation (2)

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