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 $a - c = b - d$ .

$R Q - Z Q = T P - Z P$

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 $R Z = R Q - Z Q$ .

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

Step 3. Apply Substitution property.

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

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

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. $R Q - Z Q = T P - Z P$	2. Subtraction property
3. $\begin{matrix} R Z = R Q - Z Q; \\ T Z = T P - Z P \end{matrix}$	3. Segment subtraction postulate
4. $R Z = T Z$	4. Substitution property

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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.

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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

Logic and Functions

Calculus

Discrete Mathematics

Statistics

Mechanics Maths

Applied Mathematics

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: $R Z = T Z$