Q14 Alan tried to prove Postulate 10... [FREE SOLUTION]

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 3: Q14 (page 80)

Alan tried to prove Postulate 10 as shown below. However, he did not have valid proof. Explain why not.
If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Given $k 鈭� l$ ; transversal $t$ cuts $k$ and $I$
Prove: $鈭� 1 鈮� 鈭� 2$
Statement
Reason
1. $k 鈭� l$
Given
2. $鈭� 3 鈮� 鈭� 2$
If two parallel lines are cut by transversal then alt. int. $鈭� s$ are $鈮�$
3. $鈭� 1 鈮� 鈭� 3$
Vert. $鈭� s$ are $鈮�$
4. $鈭� 1 鈮� 鈭� 2$
Transitive Property

Expert verified

Alan鈥檚 proof is not valid because he did not use transitive property correctly

If $a = b$ and $b = c$ then $a = c$

Substitute $鈭� 1$ for $a, 鈭� 3$ for $b$ , and $鈭� 2$ for $c$

From 2nd statement $b = c$

From 3rd statement $a = b$

And result concluded in 4th statement is $a = c$

Thus, transitive property is applied incorrectly

Interchange statement 2 and 3

Statement	Reason
1. $k 鈭� l$	Given
2. $鈭� 1 鈮� 鈭� 3$	Vert. $鈭� s$ are $鈮�$
3. $鈭� 3 鈮� 鈭� 2$	If two parallel lines are cut by transversal then alt. int. $鈭� s$ are $鈮�$
4. $鈭� 1 鈮� 鈭� 2$	Transitive Property