Question

1. A biconditional statement says, "A polygon is a square if and only if the polygon has

four equal sides and four right angles." Write the hypothesis and condusion.
2. A statement says, "If the measure of 4] equals the measure of K, the angles are congruent." Write the converse, inverse, and contrapositive of this statement.
3. What is the original statement if the converse of the original statement is "If a number is divisible by two, then it is an even number"? What is the inverse of the original statement?
4. Write the biconditional statement if the hypothesis is "This month is November," and the conclusion is "Next month is December."
5. A right triangle is a triangle that contains a right angle. Write the biconditional statement for the statement above. Also write the converse of the statement. Is the converse a true statement? Explain.

Answer 1

Answer:Hypothesis: A polygon has four equal sides and four right angles.

Conclusion: The polygon is a square.

Converse: If the angles are congruent, then the measure of 4] equals the measure of K.

Inverse: If the measure of 4] does not equal the measure of K, then the angles are not congruent.

Contrapositive: If the angles are not congruent, then the measure of 4] does not equal the measure of K.

Original statement: If a number is even, then it is divisible by two.

Inverse: If a number is not divisible by two, then it is not even.

Biconditional statement: This month is November if and only if next month is December.

Biconditional statement: A triangle is a right triangle if and only if it contains a right angle.

Converse: If a triangle contains a right angle, then it is a right triangle.

The converse is not necessarily a true statement as a triangle can contain a right angle and still not be a right triangle (i.e. it may not meet the requirements of all sides being of equal length).

Explanation:

Hypothesis: A polygon has four equal sides and four right angles.

Conclusion: The polygon is a square.

Converse: If the angles are congruent, then the measure of 4] equals the measure of K.

Inverse: If the measure of 4] does not equal the measure of K, then the angles are not congruent.

Contrapositive: If the angles are not congruent, then the measure of 4] does not equal the measure of K.

Original statement: If a number is even, then it is divisible by two.

Inverse: If a number is not divisible by two, then it is not even.

Biconditional statement: This month is November if and only if next month is December.

Biconditional statement: A triangle is a right triangle if and only if it contains a right angle.

Converse: If a triangle contains a right angle, then it is a right triangle.

The converse is not necessarily a true statement as a triangle can contain a right angle and still not be a right triangle (i.e. it may not meet the requirements of all sides being of equal length).