Chapter 6.3, Problem 1CE

To determine

To find: the correct way to begin the indirect proof.

Answer to Problem 1CE

The correct answer is option b.

Explanation of Solution

Given information:

An indirect proof is to be used to prove the following:

If $AB=AC$ , then $\Delta ABD\cong \Delta ACD$

Given options are,

1. Assume temporarily that $AB\ne AC$
2. Assume temporarily that $\Delta ABD\cancel{\cong }ACD$

Calculation:

Consider the following statement:

If $AB=AC$ , then $\Delta ABD\cong \Delta ACD$

An indirect proof is to be used to prove this statement.

Consider the following statements:

1. Assume temporarily that $AB\ne AC$
2. Assume temporarily that $\Delta ABD\cancel{\cong }ACD$

Write out which of the above statements is the correct way to begin the proof.

1. The correct way to begin this proof is “Assume temporarily that $\Delta ABD\cancel{\cong }ACD$".

Hence, the correct answer is option b.