Chapter 6.2, Problem 6WE

To determine

To Complete: the table by writing contrapositive, converse and inverse of the statement “ if $\angle 1\text{ and }\angle \text{2}$ are vertically opposite angles, then $m\angle 1=m\angle \text{2}$ ”.

Answer to Problem 6WE

	Statements		True
1	Contrapositive	If $m\angle 1\ne m\angle \text{2}$, then $\angle 1\text{ and }\angle \text{2}$ are not vertically opposite angles.	True
2	Converse	If $m\angle 1=m\angle \text{2}$, then $\angle 1\text{ and }\angle \text{2}$ are vertically opposite angles.	False
3	Inverse	$\angle 1\text{ and }\angle \text{2}$ are not vertically opposite angles, then $m\angle 1\ne m\angle \text{2}$.	False

Explanation of Solution

Given:

Statement is.

“ if $\angle 1\text{ and }\angle \text{2}$ are vertically opposite angles, then $m\angle 1=m\angle \text{2}$ ”.

Table is given as:

  

Calculation:

Table is completed as shown below.

	Statements		True
1	Contrapositive	If $m\angle 1\ne m\angle \text{2}$, then $\angle 1\text{ and }\angle \text{2}$ are not vertically opposite angles.	True
2	Converse	If $m\angle 1=m\angle \text{2}$, then $\angle 1\text{ and }\angle \text{2}$ are vertically opposite angles.	False
3	Inverse	$\angle 1\text{ and }\angle \text{2}$ are not vertically opposite angles, then $m\angle 1\ne m\angle \text{2}$.	False