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

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

#### Solutions

Chapter
Section ### 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 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.

MNPQ 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=MQMN

Substitute MQMN for NQ in equation (2)

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