Q13 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: Q13 (page 42)

Copy everything shown and write a two-column proof.
Given: $R Q = T P;$
$Z Q = Z P$
Prove: $R Z = T Z$

Short Answer

Expert verified

Statements	Reasons
1.	Given
2.	2. Subtraction property
3.	3. Segment subtraction postulate
4.	4. Substitution property

Step by step solution

Step 1. Apply subtraction property of algebra.

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

$R Q 鈭� Z Q = T P 鈭� Z P$

Step 2. Apply segment subtraction postulate.

From the given figure, it can be observed that difference between $R Q$ and $Z Q$ gives $R Z$ , that is $R Z = R Q 鈭� Z Q$ .

From the given figure, it can be observed that difference between $T P$ and $Z P$ gives $T Z$ , that is $T Z = T P 鈭� Z P$ .

Step 3. Apply Substitution property.

Substitute $R Z$ for $R Q 鈭� Z Q$ and $T Z$ for $T P 鈭� Z P$ in step 1.

$\begin{matrix} R Q 鈭� Z Q = T P 鈭� Z P \\ R Z = T Z \end{matrix}$

Hence, it is proved that $R Z = T Z$ .

Step 4. Write a two-column proof.

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

Statements	Reasons
1. $\begin{matrix} R P = T Q; \\ P S = Q S \end{matrix}$	Given
2. $R Q 鈭� Z Q = T P 鈭� Z P$	2. Subtraction property
3. $\begin{matrix} R Z = R Q 鈭� Z Q; \\ T Z = T P 鈭� Z P \end{matrix}$	3. Segment subtraction postulate
4. $R Z = T Z$	4. Substitution property

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Statement	Reasons
1. A, M, and B have coordinated a, x, and b respectively; $b > a$ .	1. ?
2. $A M = x 鈭� a; M B = b 鈭� x$	2. ?
3. M is the midpoint of $\overset{炉}{A B}$ .	3. ?
4. $\overset{炉}{A M} 鈮� \overset{炉}{M B}$ , or $A M = M B$	4. ?
5. $x 鈭� a = b 鈭� x$	5. ?
6. $2 x =$ ?	6. ?
7. $x = \frac{a + b}{2}$	7. ?

91影视

Copy everything shown and write a two-column proof.
Given: $R Q = T P;$
$Z Q = Z P$
Prove: $R Z = T Z$

Short Answer

Step by step solution

Step 1. Apply subtraction property of algebra.

Step 2. Apply segment subtraction postulate.

Step 3. Apply Substitution property.

Step 4. Write a two-column proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

Pure Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

91影视

Copy everything shown and write a two-column proof.Given:RQ=TP;ZQ=ZPProve:RZ=TZ

Short Answer

Step by step solution

Step 1. Apply subtraction property of algebra.

Step 2. Apply segment subtraction postulate.

Step 3. Apply Substitution property.

Step 4. Write a two-column proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

Pure Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Copy everything shown and write a two-column proof.
Given: $R Q = T P;$
$Z Q = Z P$
Prove: $R Z = T Z$