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For each statement in Ex 5-10 copy and complete a table like the one shown below.

If ∠1and ∠2are vertical angles, then m∠1=m∠2.

Short Answer

Expert verified

Statement

If ?, then ?

True/false

1. Given

If ∠1and ∠2are vertical angles, then m∠1=m∠2.

True

2. Contrapositive

If m∠1≠m∠2then ∠1and ∠2are not vertically opposite angles.

True

3. Converse

If m∠1=m∠2then ∠1and ∠2are vertical angles.

False

4. Inverse

If ∠1and ∠2are not vertically opposite angles then m∠1≠m∠2.

False

Step by step solution

01

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’â¶Ä™.

If the given statement is ‘’If p then q’’, the converse is ‘’If q then p’â¶Ä™.

If the given statement is ‘’If p then q’’, the inverse is ‘’If not p then not q’â¶Ä™.

02

Step 2. Contrapositive of the given statement

The given statement is If ∠1and ∠2are the vertical angles, thenm∠1=m∠2

and this is true.

Since vertical angles are always equal.

Therefore, the given statement: If ∠1and ∠2are vertical angles, then m∠1=m∠2is true.

The contrapositive of the given statement is If m∠1≠m∠2then ∠1and ∠2are not vertically opposite angles.

Thus, it is also true.

03

Step 3. Check inverse and converse of the given statement

The converse of the given statement is if m∠1=m∠2, then ∠1, and ∠2are vertical angles.

Thus, it is false.

The inverse of the given statement is ∠1and ∠2are not vertically opposite angles then m∠1≠m∠2.

Thus, it is false.

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