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Q28

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Found in: Page 32

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

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# Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.P is the midpoint of $\overline{GH}$ implies that $GH=2PG$.

The statement "p is the midpoint of $\overline{GH}$ implies that $GH=2PG$” is true.

The converse of the given statement “if $GH=2PG$, then P is the midpoint of $\overline{GH}$ .” is true.

See the step by step solution

## Step 1. Converse a conditional.

The converse of the conditional is obtained by interchanging the hypothesis and the conclusion. If p represents the hypothesis and q represents the conclusion, then converse of the statement “If p, then q” will be “If q, then p”.

## Step 2. State whether the statement is true or not.

The statement "P is the midpoint of $\overline{GH}$ implies that $GH=2PG$”, P is the midpoint of $\overline{GH}$

That is:

$\begin{array}{c}GH=GP+PH\\ =2PG\end{array}$

Therefore, the statement is true.

## Step 3. Write the converse and verify if it is true or not.

The converse is of the form "if q, then p”.

Further, here p is P is the midpoint of $\overline{GH}$ and q is $GH=2PG$.

Therefore, the converse of the given statement is – “If $GH=2PG$ then, P is the midpoint of $\overline{GH}$.”

Here $GH=2PG$

$GH=2PG$

$=PG+PG$

$=GP+PH$

Then P is the midpoint of $\overline{GH}$.

Therefore, the converse of the given statement is true.

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