Consider triangle FGH. Line JK is constructed parallel to line segment FH. From this, the table shows a proof for the statement mzGFH+ MŁFGH+ mzFHG= 180°.StatementJustificationStepGivenAngle Addition PostulateLine JK is parallel to line segment FH.MZFGH+ MZHGK= mzFGKMJGF + mzFGK = 180°mzJGF+ MLFGH+ MLHGK= 180°ZFHGE LKGH, and LGFH LFGJ11Substitution46.mzF+ mzG+ mLH= 180°SubstitutionWhat are the missing justifications in the proof?Step 3: Definition of adjacent anglesStep 5: Alternate Exterior Angles TheoremStep 3: Definition of adjacent anglesStep 5: Alternate Interior Angles TheoremStep 3: Definition of a linear pairStep 5: Alternate Exterior Angles TheoremStep 3: Definition of a linear pairStep 5: Alternate Interior Angles TheoremA Calculator

Answered: Consider triangle FGH. Line JK is…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Consider triangle FGH. Line JK is constructed parallel to line segment FH. From this, the table shows a proof for the statement mzGFH+ MŁFGH+ mzFHG= 180°.
Statement
Justification
Step
Given
Angle Addition Postulate
Line JK is parallel to line segment FH.
MZFGH+ MZHGK= mzFGK
MJGF + mzFGK = 180°
mzJGF+ MLFGH+ MLHGK= 180°
ZFHGE LKGH, and LGFH LFGJ
11
Substitution
4
6.
mzF+ mzG+ mLH= 180°
Substitution
What are the missing justifications in the proof?
Step 3: Definition of adjacent angles
Step 5: Alternate Exterior Angles Theorem
Step 3: Definition of adjacent angles
Step 5: Alternate Interior Angles Theorem
Step 3: Definition of a linear pair
Step 5: Alternate Exterior Angles Theorem
Step 3: Definition of a linear pair
Step 5: Alternate Interior Angles Theorem
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Expert Solution

Step 1

Given,

JK || FH

m∠GFH + m∠FGH + m∠FHG = 180°

According to given,

Step 3:

From the diagram we can clearly observe that,

m∠JFG + m∠FGK = 180°

A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines.A linear pair of angles must add up to 180 degrees.

The above statement, satisfies this condition.

Therefore,

m∠JFG + m∠FGK = 180° is a definition of linear pair.

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