Question

use the law of syllogism to write four conditional statements that can be formed from the following true statements.
a. if a quadrilateral is a square, then it has four right angles.
b. if a quadrilateral is a rhombus, then its opposite sides are parallel.
c. if a quadrilateral is a parallelogram, then its opposite angles are congruent.
d. if a quadrilateral has four right angles, then it is a rectangle.
e. if a quadrilateral is a rectangle, then its opposite sides are congruent.
f. if the opposite sides of a quadrilateral are parallel, then it is a parallelogram.
statement 1:

statement 2:

statement 3:

statement 4:

Explanation:

Statement 1:

Combine statement a and d.
If a quadrilateral is a square (from a), then it has four right angles (from a). And if a quadrilateral has four right angles (from d), then it is a rectangle (from d). By the Law of Syllogism: If a quadrilateral is a square, then it is a rectangle.

Statement 2:

Combine statement d and e.
If a quadrilateral has four right angles (from d), then it is a rectangle (from d). And if a quadrilateral is a rectangle (from e), then its opposite sides are congruent (from e). By the Law of Syllogism: If a quadrilateral has four right angles, then its opposite sides are congruent.

Statement 3:

Combine statement b and f.
If a quadrilateral is a rhombus (from b), then its opposite sides are parallel (from b). And if the opposite sides of a quadrilateral are parallel (from f), then it is a parallelogram (from f). By the Law of Syllogism: If a quadrilateral is a rhombus, then it is a parallelogram.

Statement 4:

Combine statement f and c.
If the opposite sides of a quadrilateral are parallel (from f), then it is a parallelogram (from f). And if a quadrilateral is a parallelogram (from c), then its opposite angles are congruent (from c). By the Law of Syllogism: If the opposite sides of a quadrilateral are parallel, then its opposite angles are congruent.

Answer:

Statement 1: If a quadrilateral is a square, then it is a rectangle.
Statement 2: If a quadrilateral has four right angles, then its opposite sides are congruent.
Statement 3: If a quadrilateral is a rhombus, then it is a parallelogram.
Statement 4: If the opposite sides of a quadrilateral are parallel, then its opposite angles are congruent.