Q2 State which definition, postulat... [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 2: Q2 (page 46)

State which definition, postulate, or theorem justifies the statement about the diagram.
If $鈭� 1 鈮� 鈭� 2$ , then $\overset{鈫�}{A D}$ is the bisector of $鈭� B A C$ .

Short Answer

Expert verified

The angle bisector theorem justifies the statement about the diagram.

Step by step solution

Step 1. Observe the given diagram.

The diagram constitutes a triangle ABC and $鈭� 1 鈮� 鈭� 2$ .

Step 2. State the angle bisector theorem.

The theorem states that if a line bisects an angle of a triangle, then that line divides the opposite side of that angle into two segments proportional to other two sides of the triangle.

Step 3. State the conclusion.

Considering the given diagram and the statement: 鈥渋f $鈭� 1 鈮� 鈭� 2$ then $\overset{鈫�}{A D}$ is the bisector of $鈭� B A C$ 鈥�.

Therefore, the statement about the diagram is justified by the angle bisector theorem.

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Statement	Reasons
1. $\overset{鈫�}{B X}$ is the bisector of $鈭� A B C$	1. ?
2. $鈭� A B X 鈮�$ ?, or $m 鈭� A B X =$ ?	2. ?
3. $m 鈭� A B X + m 鈭� X B C = m 鈭� A B C$	3. ?
4. $m 鈭� A B X + m 鈭� A B X = m 鈭� A B C$ , or $2 m 鈭� A B X = m 鈭� A B C$	4. ?
5. $m 鈭� A B X = \frac{1}{2} m 鈭� A B C$	5. ?
6. $m 鈭� X B C = \frac{1}{2} m 鈭� A B C$	6. Substitution Prop. (Steps ? and ?)

91影视

State which definition, postulate, or theorem justifies the statement about the diagram.
If $鈭� 1 鈮� 鈭� 2$ , then $\overset{鈫�}{A D}$ is the bisector of $鈭� B A C$ .

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. State the angle bisector theorem.

Step 3. State the conclusion.

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91影视

State which definition, postulate, or theorem justifies the statement about the diagram.If 鈭�1鈮�鈭�2, then AD鈫� is the bisector of 鈭�BAC.

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. State the angle bisector theorem.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

State which definition, postulate, or theorem justifies the statement about the diagram.
If $鈭� 1 鈮� 鈭� 2$ , then $\overset{鈫�}{A D}$ is the bisector of $鈭� B A C$ .