McDougal Littell Jurgensen Geometry: Student Edition Geometry
McDougal Littell Jurgensen Geometry: Student Edition Geometry
5th Edition
ISBN: 9780395977279
Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Publisher: Houghton Mifflin Company College Division
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Chapter 3.4, Problem 15CE
To determine

To prove: If an angle is exterior to a triangle, then its measure equals the sum of the measures of the two remote interior angles by using the equations:

  m1+m2+m3=180(1) ,

  m3+m4=180(2)

Expert Solution & Answer
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Explanation of Solution

Given information:

  ΔABC and its angles.

Proof:

Theorem 3-12:- If an angle is exterior to a triangle, then its measure equals the sum of the measures of the two remote interior angles.

  McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.4, Problem 15CE

As per Theorem, you need to prove that

  m1+m2=m4....(3)

From equation (1)

  m1+m2+m3=180m1+m2=180m3.....(4)

From equation (2),

  m3+m4=180

  m4=180m3....(5)

Putting the value of equation (5) in equation (4), you get

  m1+m2=m4

Hence, the theorem is proved.

Therefore, the given equation can be used to prove Theorem 3-12.

Chapter 3 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

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