Question

name: liderson santos date: 10/2/2025 period:
warm - up/ bell ringer for thursday (10 - 09 - 2025)
question 1. (similar to usa2 from ma.912.lt.4.3)
if the polygon is a triangle, then the interior angle measures sum is 180°

	biconditional	converse	inverse	contra - positive
if the polygon is not a triangle, then the interior angle measures sum is not 180°.
if the interior angle measures sum is not 180°, then the polygon is not a triangle.
if the interior angle measures sum is 180°, then the polygon is a triangle.

Explanation:

Step1: Recall conditional statement forms

Let the original statement be "If \(p\) (the polygon is a triangle), then \(q\) (the interior - angle measures sum is \(180^{\circ}\))". The biconditional is \(p\) if and only if \(q\), the converse is "If \(q\), then \(p\)", the inverse is "If not \(p\), then not \(q\)", and the contra - positive is "If not \(q\), then not \(p\)".

Step2: Analyze each statement

1. "The polygon is a triangle, if and only if, the interior angle measures sum is \(180^{\circ}\)" is the biconditional.
2. "If the polygon is not a triangle, then the interior angle measures sum is not \(180^{\circ}\)" is the inverse.
3. "If the interior angle measures sum is not \(180^{\circ}\), then the polygon is not a triangle" is the contra - positive.
4. "If the interior angle measures sum is \(180^{\circ}\), then the polygon is a triangle" is the converse.

Answer:

Statement	Biconditional	Converse	Inverse	Contra - positive
If the polygon is not a triangle, then the interior angle measures sum is not \(180^{\circ}\)			\(\checkmark\)
If the interior angle measures sum is not \(180^{\circ}\), then the polygon is not a triangle				\(\checkmark\)
If the interior angle measures sum is \(180^{\circ}\), then the polygon is a triangle		\(\checkmark\)