Geometry - 2.4 Deductive Reasoning

If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

Statement 1: If x = 7, then 7x – 2 = 47.

Statement 2: x = 7

• x = 7

• If 7x – 2 = 47, then x = 7.

• 7x – 2 = 47

• not possible

Use the Law of Detachment to draw a conclusion from the two given statements.

If two angles are complementary, then the sum of their measures is 90°.

∠E and ∠F are complementary.

• m∠E + m∠F = 180

• ∠E is congruent to ∠F.

• m∠E ≠ m∠F

• m∠E + m∠F = 90

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

I can go to the concert if I can afford to buy a ticket.

I can go to the concert.

• I can afford to buy a ticket.

• I cannot afford to buy the ticket.

• If I can go to the concert, I can afford the ticket.

• not possible

Use the Law of Syllogism to draw a conclusion from the two given statements.

If you exercise regularly, then you have a healthy body.

If you have a healthy body, then you have more energy.

• If you do not have more energy, then you do not exercise regularly.

• You have more energy.

• You have a healthy body.

• If you exercise regularly, then you have more energy.

Which statement is the Law of Syllogism?

• A. If p → q is a true statement and p is true, then q is true.

• B. If p → q is a true statement and q is true, then p is true.

• C. If p → q and q → r are true statements, then p → r is a true statement.

• D. If p → q and q → r are true statements, then r → p is a true statement.

Use the Law of Syllogism to draw a conclusion from the two given statements.

If two lines intersect and form right angles, then the lines are perpendicular.

If two lines are perpendicular, then they intersect and form 90° angles.

• The lines are perpendicular.

• If two lines intersect and form right angles, then they intersect and form 90° angles.

• The lines intersect and form 90° angles.

• If two lines do not intersect and form 90° angles, then they do not form right angles.

Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements.

If it is Friday night, then there is a football game.

If there is a football game, then Josef is wearing his school colors.

It is Friday night.

• If it is Friday night, then Josef is wearing his school colors.

• Josef is wearing his school colors.

• There is a football game.

• If it is not Friday night, then Josef is not wearing his school colors.

Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements.

If an elephant weighs more than 2000 pounds, then it weighs more than Jill’s car.

If something weighs more than Jill’s car, then it is too heavy for the bridge.

Smiley the elephant weighs 2150 pounds.

• Smiley is too heavy for the bridge.

• Smiley weighs more than Jill’s car.

• If Smiley weighs more than 2000 pounds, then Smiley is too heavy for the bridge.

• If Smiley weighs more than Jill’s car, then Smiley is too heavy for the bridge.

Which statement is the Law of Detachment?

• If p → q is a true statement and q is true, then p is true.

• If p → q is a true statement and q is true, then q → p is true.

• If p → q and q → r are true, then p → r is a true statement.

• p → q is a true statement and p is true, then q is true.