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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 3: Q29. (page 115)

Name or state the postulate, definition, or theorem that justifies each statement about the diagram.
$m ∠ 1 + m ∠ 2 = m ∠ A B C$

Short Answer

Expert verified

The postulate that justifies the given statement is the Angle Addition Postulate.

Step by step solution

01

Step 1. Find the interior angles of ∠ABC.

Observe that both the angles ∠1 and ∠2 are interior of $∠ A B C$ .

02

Step 2. Determine the theorem or postulate that can be used.

Postulate 4, the Angle Addition Postulate, states that if lies in the interior of $∠ A O C$ , then $m ∠ A O B + m ∠ B O C = m ∠ A O C$ .

03

Step 3. Use the postulate.

So, the sum of the angles∠1and ∠2 is equal to $∠ A B C$ by the angle addition postulate.

That is, $m ∠ 1 + m ∠ 2 = m ∠ A B C$ .

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Most popular questions from this chapter

Draw each figure described.

Lines d and e are skew, lines e and f are skew, and $d ⊥ f$ .

Complete each statement with the word always, sometimes, or never.

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Complete each statement with the word always, sometimes, or never. A line in the plane of the ceiling and a line in the plane of the floor are parallel.

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