Question

2-2a practice worksheet - biconditionals and definitions
a biconditional statement combines a conditional statement, “if p, then q,” with its converse, “if q, then p.”
conditional: if the sides of a triangle are congruent, then the angles are congruent.
converse: if the angles of a triangle are congruent, then the sides are congruent.
biconditional: the sides of a triangle are congruent if and only if the angles are congruent.
...where p = hypothesis and q = conclusion
for each conditional, write the converse and a biconditional statement.

1. conditional: if the date is july 4th, then it is independence day.

converse:
biconditional:

1. conditional: if a figure has 10 sides, then it is a decagon.

converse:
biconditional:
write each definition as a biconditional.
3.an isosceles triangle has at least two congruent sides.

1. a cube is a three - dimensional solid with six square faces.

Explanation:

Step1: Recall the concept of converse

Switch the hypothesis and conclusion of the conditional statement.

Step2: Recall the concept of biconditional

Combine the conditional and its converse using "if and only if".

1.

• Converse: If it is Independence Day, then the date is July 4th.
• Biconditional: The date is July 4th if and only if it is Independence Day.

2.

• Converse: If a figure is a decagon, then it has 10 sides.
• Biconditional: A figure has 10 sides if and only if it is a decagon.

1. A triangle is an isosceles triangle if and only if it has at least two congruent sides.
2. A solid is a cube if and only if it is a three - dimensional solid with six square faces.

Answer:

1. Converse: If it is Independence Day, then the date is July 4th.

Biconditional: The date is July 4th if and only if it is Independence Day.

1. Converse: If a figure is a decagon, then it has 10 sides.

Biconditional: A figure has 10 sides if and only if it is a decagon.

1. A triangle is an isosceles triangle if and only if it has at least two congruent sides.
2. A solid is a cube if and only if it is a three - dimensional solid with six square faces.