Q23. Copy everything shown. Complete ... [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: Q23. (page 53)

Copy everything shown. Complete the proof.
Given: $鈭� 2 鈮� 鈭� 3$
Prove: $鈭� 1 鈮� 鈭� 4$
Proof:

Short Answer

Expert verified

statements	Reasons
1. $鈭� 1 鈮� 鈭� 2$	1. vertical angles
2. $鈭� 2 鈮� 鈭� 3$	2. Given
3. $鈭� 3 鈮� 鈭� 4$	3. vertical angles
4. $鈭� 1 鈮� 鈭� 4$	4. Transitive property (used twice)

Step by step solution

Step 1. Write the relation between the angles ∠1 and ∠2.

From the given diagram it can be noticed that the angles $鈭� 1$ and $鈭� 2$ are vertical angles, therefore the angles $鈭� 1$ and $鈭� 2$ are congruent angles.

Step 2. Write the relation between the angles ∠2 and ∠3.

The angles $鈭� 2$ and $鈭� 3$ are congruent angles as it is given that $鈭� 2 鈮� 鈭� 3$ .

Step 3. Write the relation between the angles ∠3 and ∠4.

From the given diagram it can be noticed that the angles $鈭� 3$ and $鈭� 4$ are vertical angles, therefore the angles $鈭� 3$ and $鈭� 4$ are congruent angles.