Download ANSWER KEY: A conditional statement can be written in the form “if

 ANSWER KEY: A conditional statement can be written in the form “if P, then Q.” This “if, then” statement can be true or false. The “if” part is called the hypothesis and the “then” part is called the conclusion. To write the converse of the conditional statement, switch the hypothesis and the conclusion. To write the inverse of the conditional statement, negate the hypothesis and the conclusion. To write the contrapositive of the conditional statement, swap the hypothesis and conclusion and negate both. 1. Question One: •
Conditional Statement: If an animal is a cow, then is has four legs. True, cows have four legs. •
Converse: If an animal has four legs, then it is a cow. False, counter example: pig, dog, etc. •
Inverse: If the animal is not a cow, then it does not have four legs. False, animals besides cows have four legs. C.E. Dog, Cat, etc. •
Contrapositive: If the animal does not have four legs, then it is not a cow. True, cows must have four legs. 2. Question Two: •
Conditional Statement: If a quadrilateral is a rhombus, then it has four congruent sides. True. This is the definition of a rhombus. •
Converse: If a quadrilateral has four congruent sides, then it is a rhombus. True. This is the definition of a rhombus. •
Inverse: If a quadrilateral is not a rhombus, then it does not have four congruent sides. True. This is true by the definition of a rhombus. •
Contrapositive: If a quadrilateral does not have four congruent sides, then it is not a rhombus. True. This is true by the definition of a rhombus. 3. Question Three: •
Conditional Statement: If one of the acute angles of a right triangle measures 45°, then it is an isosceles right triangle. •
Converse: If a triangle is an isosceles right triangle, then one of the acute angle measures in the right triangle measures 45°. True. This base angles must be congruent in isosceles triangles and the interior angles in a triangle must add to 180°. •
Inverse: If one of the acute angles of a right triangle does not measure 45°, then it is not an isosceles right triangle. True. Right Isosceles Triangles must have two congruent base angles, each measuring 45°. If one doesn’t measure 45°, then it is either not an isosceles triangle or it is not a right triangle. •
Contrapositive: If a triangle is not an isosceles right triangle, then it is not a right triangle with an acute angle that measures 45°. True. The acute angles in a right triangle add to 90°, since base angles are congruent in isosceles triangles, they have to be the same measure, meaning both are 45°. If one of the acute angles is not 45° then there is no way base angles can be congruent. 4. Question Four: •
Conditional Statement: If two angles are vertical angles, then they are congruent. •
Converse: If two angles are congruent, then the two angles are vertical. False. Two angles can be congruent without being vertical angles. Counterexample: alternate interior angles. •
Inverse: If two angles are not vertical angles, then they are not congruent. False. Alternate Exterior angles are not vertical angles and they are congruent. •
Contrapositive: If two angles are not congruent, then they are not vertical angles. True. In order to be vertical angles, the angle pair must be congruent.