Chapter 2: Q8 (page 34)
Provide a counterexample to show that each statement is false. You may use words or draw a diagram.
If 
, then B is the midpoint of 
.
Short Answer
The counterexample is the Equilateral triangle.
Step by step solution
Step 1. Define counterexample.
The counterexample is an example for which a hypothesis is true but the conclusion is false for an if-then statement.
Step 2. Observation of the statement.
In order to find a counterexample for the statement “If 
, then B is the midpoint of 
.” we need to find two lines 
and
such that they are equal to each other but B is not the midpoint 
.
Step 3. State the counterexample.
The equilateral triangle is the counterexample.
In, equilateral triangle line segment 
and 
are congruent but point B is not in 
, so it cannot be its midpoint.
Therefore, the counterexample is an Equilateral triangle.
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if S is the midpoint of
.
