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Answers without the blur. Sign up and see all textbooks for free! Q7.

Expert-verified Found in: Page 211 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # For each statement in Ex 5-10 copy and complete a table like the one shown below. If $AM=MB$, then M is the midpoint of $\overline{AB}$.

 Statement If ?, then ? True/false 1. Given If $AM=MB$, then M is the midpoint of $\overline{AB}$. False 2. Contrapositive If M is not a midpoint of $\overline{AB}$ then $AM\ne MB$. False 3. Converse If M is the midpoint of $\overline{AB}$ then role="math" localid="1638260520254" $AM=MB$. True 4. Inverse If $AM\ne MB$, then M is not the midpoint of $\overline{AB}$. False
See the step by step solution

## Step 1. Define contrapositive, inverse, and converse for the given statement

If the given statement is ‘’If p then q’’, the contrapositive is ‘’If not q then not p’’.

If the given statement is ‘’If p then q’’, the converse is ‘’If q then p’’.

If the given statement is ‘’If p then q’’, the inverse is ‘’If not p then not q’’.

## Step 2. Contrapositive of the given statement

The given statement is If $AM=MB$, then M is the midpoint of $\overline{AB}$.

If A, M, and B are non-collinear for example vertex of an equilateral triangle.

Therefore, the given statement: If $AM=MB$, then M is the midpoint of $\overline{AB}$

is false.

Suppose A, M, and B are the vertex of an equilateral triangle.

The contrapositive of the given statement is If M is not a midpoint of $\overline{AB}$ then $AM\ne MB$.

Thus, it is also false.

## Step 3. Check inverse and converse of the given statement

Since the midpoint is equidistant from both the endpoints of the line segment.

The converse of the given statement is If M is the midpoint of $\overline{AB}$ then $AM=MB$.

Thus, it is true.

The inverse of the given statement is If $AM\ne MB$, then M is not the midpoint of the line segment $\overline{AB}$.

Thus, it is false. ### Want to see more solutions like these? 