Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![**Find the missing part of the proof for \( m \angle PQR = 105^\circ \) and \( m \angle PQT = 27^\circ \).**
**Diagram:**
A geometric diagram shows three points labeled Q, P, and R, forming angles PQR and PQT. The lines originate from point P, with an arrow indicating direction.
**Proof:**
**Statements:**
1. \( m \angle PQR = 105^\circ \)
2. \( m \angle PQT = 27^\circ \)
3. [Missing statement]
4. \( 27^\circ + m \angle TQR = 105^\circ \)
5. \( 27^\circ + m \angle TQR - 27^\circ = 105^\circ - 27^\circ \)
6. \( m \angle TQR = 78^\circ \)
**Reasons:**
1. Given
2. Given
3. [Missing reason]
4. Substitution
5. Subtraction property of equality
6. Simplify
**Answer Choices for the Missing Parts:**
- \( m \angle PQR + m \angle PQT = m \angle TQR, \) Angle Addition Postulate
- \( m \angle PQT + m \angle PQR = m \angle TQR, \) Segment Addition Postulate
- \( m \angle PQT + m \angle TQR = m \angle PQR, \) Angle Addition Postulate
- \( m \angle PQT + m \angle TQR = m \angle PQR, \) Segment Addition Postulate
The correct choice to complete the proof statement and reason is:
- \( m \angle PQT + m \angle TQR = m \angle PQR, \) Angle Addition Postulate](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb92c0de6-daa1-4ec9-9e5b-05e29c727673%2F3d2e844f-5631-4a63-ab36-87fcc6881c27%2Fz4z165o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the missing part of the proof for \( m \angle PQR = 105^\circ \) and \( m \angle PQT = 27^\circ \).**
**Diagram:**
A geometric diagram shows three points labeled Q, P, and R, forming angles PQR and PQT. The lines originate from point P, with an arrow indicating direction.
**Proof:**
**Statements:**
1. \( m \angle PQR = 105^\circ \)
2. \( m \angle PQT = 27^\circ \)
3. [Missing statement]
4. \( 27^\circ + m \angle TQR = 105^\circ \)
5. \( 27^\circ + m \angle TQR - 27^\circ = 105^\circ - 27^\circ \)
6. \( m \angle TQR = 78^\circ \)
**Reasons:**
1. Given
2. Given
3. [Missing reason]
4. Substitution
5. Subtraction property of equality
6. Simplify
**Answer Choices for the Missing Parts:**
- \( m \angle PQR + m \angle PQT = m \angle TQR, \) Angle Addition Postulate
- \( m \angle PQT + m \angle PQR = m \angle TQR, \) Segment Addition Postulate
- \( m \angle PQT + m \angle TQR = m \angle PQR, \) Angle Addition Postulate
- \( m \angle PQT + m \angle TQR = m \angle PQR, \) Segment Addition Postulate
The correct choice to complete the proof statement and reason is:
- \( m \angle PQT + m \angle TQR = m \angle PQR, \) Angle Addition Postulate
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