Q7. Write the reasons that justify t... [FREE SOLUTION]

91影视

Geometry

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

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 6: Q7. (page 206)

Write the reasons that justify the statements.
Given: $\overset{鈫�}{D E}, \overset{鈫�}{F G}, \overset{鈫�}{Z H}$ contain point Z. Prove: $m 鈭� D Z H > m 鈭� G Z E$

Short Answer

Expert verified

Statement	Proof
1. $鈭� D Z F 鈮� 鈭� G Z E$ or $m 鈭� D Z F = m 鈭� G Z E$	Vertically opposite angles are always congruent or their measures are equal.
2. $m 鈭� D Z H = m 鈭� D Z F + m 鈭� F Z H$	$\overset{鈫�}{Z F}$ divides $鈭� D Z H$ into two parts as $鈭� D Z F$ and $鈭� F Z H$
3. $m 鈭� D Z H > m 鈭� D Z F$	The whole angle is bigger than its own parts.
4. $m 鈭� D Z H > m 鈭� G Z E$	Statement 1,2, and 3.

Step by step solution

Step 1. Draw the given diagram and define the congruent property of angles

Vertically opposite angles are always congruent or their measures are equal.

Step 2. Use property of vertically opposite angles

Since vertically opposite angles are always congruent or their measures are equal. Therefore, $鈭� D Z F 鈮� 鈭� G Z E$ or $m 鈭� D Z F = m 鈭� G Z E$

Step 3. Prove the statement

From the figure, $\overset{鈫�}{Z F}$ divides $鈭� D Z H$ into two parts as $鈭� D Z F$ and $鈭� F Z H$ .

Therefore, $m 鈭� D Z H = m 鈭� D Z F + m 鈭� F Z H$ .

Since, whole angles is always bigger than its own parts, therefore $m 鈭� D Z H > m 鈭� D Z F$ .

As $m 鈭� D Z H = m 鈭� D Z F + m 鈭� F Z H$ and by statement 1 $鈭� D Z F = 鈭� G Z E$ . Therefore, statement 1, 2 and 3 shows that $m 鈭� D Z H > m 鈭� G Z E$ .

Hence, $m 鈭� D Z H > m 鈭� G Z E$ is proven with suitable reasons.

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91影视

Write the reasons that justify the statements.
Given: $\overset{鈫�}{D E}, \overset{鈫�}{F G}, \overset{鈫�}{Z H}$ contain point Z. Prove: $m 鈭� D Z H > m 鈭� G Z E$

Short Answer

Step by step solution

Step 1. Draw the given diagram and define the congruent property of angles

Step 2. Use property of vertically opposite angles

Step 3. Prove the statement

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91影视

Write the reasons that justify the statements.Given: DE鈫�,FG鈫�,ZH鈫� contain point Z. Prove: m鈭�DZH>m鈭�GZE

Short Answer

Step by step solution

Step 1. Draw the given diagram and define the congruent property of angles

Step 2. Use property of vertically opposite angles

Step 3. Prove the statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Statistics

Pure Maths

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

Write the reasons that justify the statements.
Given: $\overset{鈫�}{D E}, \overset{鈫�}{F G}, \overset{鈫�}{Z H}$ contain point Z. Prove: $m 鈭� D Z H > m 鈭� G Z E$