Q14 Copy everything shown and write ... [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: Q14 (page 42)

Copy everything shown and write a two-column proof.
Given: $m 鈭� S R T = m 鈭� S T R;$
$m 鈭� 3 = m 鈭� 4$
Proof: $m 鈭� 1 = m 鈭� 2$

Short Answer

Expert verified

Statements	Reasons
1.	Given
2.	2. Angle addition postulate
3.	3. Substitution property
4.	4. Given
5.	5. Subtraction property

Step by step solution

Step 1. Angle addition postulate.

From the given figure, it can be observed that sum of $m 鈭� 1$ and $m 鈭� 3$ gives $m 鈭� S R T$ , that is $m 鈭� 2 + m 鈭� 4 = m 鈭� S T R$ .

From the given figure, it can be observed that sum of $m 鈭� 2$ and $m 鈭� 4$ gives $m 鈭� S T R$ , that is $m 鈭� 2 + m 鈭� 4 = m 鈭� S T R$ .

Step 2. Apply substitution property.

Substitute $m 鈭� 1 + m 鈭� 3$ for $m 鈭� S R T$ and $m 鈭� 2 + m 鈭� 4$ for in $m 鈭� S T R$ .

$\begin{matrix} m 鈭� S R T = m 鈭� S T R \\ m 鈭� 1 + m 鈭� 3 = m 鈭� 2 + m 鈭� 4 \end{matrix}$

Step 3. Apply the subtraction property of algebra.

If $a = b$ and $c = d$ , then $a 鈭� c = b 鈭� d$ .

$m 鈭� 1 = m 鈭� 2$

Step 4. Write a two-column proof.

Write a two-column proof with the help of the above-mentioned steps.

Statements	Reasons
1. $m 鈭� S R T = m 鈭� S T R$	Given
2. $\begin{matrix} m 鈭� 1 + m 鈭� 3 = m 鈭� S R T; \\ m 鈭� 2 + m 鈭� 4 = m 鈭� S T R \end{matrix}$	2. Angle addition postulate
3. $m 鈭� 1 + m 鈭� 3 = m 鈭� 2 + m 鈭� 4$	3. Substitution property
4. $m 鈭� 3 = m 鈭� 4$	4. Given
5. $m 鈭� 1 = m 鈭� 2$	5. Subtraction property

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91影视

Copy everything shown and write a two-column proof.
Given: $m 鈭� S R T = m 鈭� S T R;$
$m 鈭� 3 = m 鈭� 4$
Proof: $m 鈭� 1 = m 鈭� 2$

Short Answer

Step by step solution

Step 1. Angle addition postulate.

Step 2. Apply substitution property.

Step 3. Apply the subtraction property of algebra.

Step 4. Write a two-column proof.

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91影视

Copy everything shown and write a two-column proof.Given:m鈭�SRT=m鈭�STR;m鈭�3=m鈭�4Proof:m鈭�1=m鈭�2

Short Answer

Step by step solution

Step 1. Angle addition postulate.

Step 2. Apply substitution property.

Step 3. Apply the subtraction property of algebra.

Step 4. Write a two-column proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Pure Maths

Geometry

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Copy everything shown and write a two-column proof.
Given: $m 鈭� S R T = m 鈭� S T R;$
$m 鈭� 3 = m 鈭� 4$
Proof: $m 鈭� 1 = m 鈭� 2$