the other statements are.
- Converse: If it has a perimeter of 10 cm, then the figure is a rectangle with sides of 2 cm and 3 cm (false)
- Inverse: If the figure is not a rectangle with sides of 2 cm and 3 cm, then it has a perimeter different than 10cm (false)
- Contrapositive: "If it has a perimeter different than 10cm, then it is not a rectangle with sides of 2cm and 3cm" (true)
How to get the converse, inverse, and contrapositive statements?
For a conditional statement of the form:
If P, then Q
The other statements are:
- Converse: if Q then P
- Inverse: not P, then not Q.
- Contrapositive: not Q, then not P.
Here the conditional is:
"if a figure is a rectangle with sides 2 cm and 3cm, then it has a perimeter of 10cm"
We can identify:
P = a figure is a rectangle with sides 2 cm and 3cm
Q = it has a perimeter of 10cm
Then the other statements are.
- Converse: If it has a perimeter of 10 cm, then the figure is a rectangle with sides of 2 cm and 3 cm
This clearly is false, as we can have a circle with a perimeter of 10 cm.
- Inverse: If the figure is not a rectangle with sides of 2 cm and 3 cm, then it has a perimeter different than 10cm
This is also false, the figure can be a rectangle with sides of 1cm and 4 cm for example.
- Contrapositive: "If it has a perimeter different than 10cm, then it is not a rectangle with sides of 2cm and 3cm"
This is true. if the figure does not have a perimeter of 10cm, then it can't be a rectangle with sides of 2cm and 3cm
If you want to learn more about conditional statements:
https://brainly.com/question/11073037
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