# 1951 AHSME Problems/Problem 14

## Problem

In connection with proof in geometry, indicate which one of the following statements is incorrect: $\textbf{(A)}\ \text{Some statements are accepted without being proved.}$ $\textbf{(B)}\ \text{In some instances there is more than one correct order in proving certain propositions.}$ $\textbf{(C)}\ \text{Every term used in a proof must have been defined previously.}$ $\textbf{(D)}\ \text{It is not possible to arrive by correct reasoning at a true conclusion if, in the given, there is an untrue proposition.}$ $\textbf{(E)}\ \text{Indirect proof can be used whenever there are two or more contrary propositions.}$

## Solution

After reading the options, it is very apparent that $\textbf{(E)}\ \text{Indirect proof can be used whenever there are two or more contrary propositions.}$ is the correct answer; rigorous proof is needed no matter what.

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