Chapter 3.2, Problem 14CE

To determine

To find: If Alan did not have a valid proof, while proving postulate 10.

Answer to Problem 14CE

Alan`s proof is not valid as he did not use order of equality of statement, so that to show transitive property correctly.

Explanation of Solution

Given information: Postulate 10 states that if two parallel lines are cut by a transversal, then corresponding angles are congruent. So, in given figure, k is parallel to l and t cuts both of these lines. Statements given by Alan to prove $\angle 1\cong \angle 2$ are also given.

Concept used: Transitive property says that if $a=b$ and $b=c$ then $a=c$ .

Statements given by Alan in proving postulate 10 are all correct except while writing the statements for using transitive property. Alan did not write the statements correctly as per the above rule of transitive property, while making it proved by transitive property. Correct statements will be written as:

Statements	Reasons
1. $k\left|\right|l$	1. Given
2. $\angle 2\cong \angle 3$	2. If two parallel lines are cut by a transversal then alternate interior angles are congruent.
3. $\angle 3\cong \angle 1$	3. Vertical opposite angles are congruent.
4. $\angle 1\cong \angle 2$	4.Transitive property

Conclusion: So, Alan had to write the correct order of equality in above statement 2 and statement 3, so that to correctly use the transitive property to make his proof valid as shown above.