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Chapter 2: Q28 (page 32)

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

P is the midpoint ofGH炉 implies that GH=2PG.

Short Answer

Expert verified

The statement "p is the midpoint ofGH炉implies that GH=2PG鈥� is true.

The converse of the given statement 鈥渋f GH=2PG, then P is the midpoint of GH炉 .鈥� is true.

Step by step solution

01

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 鈥淚f p, then q鈥� will be 鈥淚f q, then p鈥�.

02

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

The statement "P is the midpoint ofGH炉 implies that GH=2PG鈥�, P is the midpoint of GH炉

That is:

GH=GP+PH=2PG

Therefore, the statement is true.

03

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

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

Further, here p is P is the midpoint of GH炉and q is GH=2PG.

Therefore, the converse of the given statement is 鈥� 鈥淚f GH=2PG then, P is the midpoint of GH炉.鈥�

Here GH=2PG

GH=2PG

=PG+PG

=GP+PH

Then P is the midpoint of GH炉.

Therefore, the converse of the given statement is true.

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