Help me plz Deductive Reasoning
Determine if the conclusion is valid or invalid based on the...
Mathematics, 21.02.2020 03:32 miguelturner
Help me plz Deductive Reasoning
Determine if the conclusion is valid or invalid based on the given statements and the Law of Detachment.
1. Given: If an angle measures more than 90°, then it is not acute.
m∠ABC = 120°
Conclusion: ∠ABC is not acute.
2. Given: If two angles measure 45°, then the angles are congruent.
∠XYZ ≅ ∠MNP
Conclusion: m∠XYZ = 45° and m∠MNP = 45°
3. Given: If you order the apple pie, then it will be served with ice cream.
Matthew ordered the apple pie.
Conclusion: Matthew was served ices cream.
Determine if the conclusion is valid or invalid based on the given statements and the Law of Syllogism.
4. Given: If ∠A is acute, then ∠B is obtuse.
If ∠B is obtuse, then ∠C is acute.
Conclusion: If ∠A is acute, then ∠C is acute.
5. Given: If a ray bisects a right angle, then the congruent angles formed are complementary.
If two congruent angles are complementary, then each angle has a measure of 45°.
Conclusion: If a ray bisects a right angle, then each angle has a measure of 45°.
6. Given: If two angles form a linear pair, then the two angles are supplementary.
If ∠A and ∠B are supplementary, then m∠A + m∠B = 180°
Conclusion: If m∠A + m∠B = 180°, then ∠A and ∠B form a linear pair.
Use the Law of Detachment to write the conclusion that follows from the pair of true statements.
7. If the sum of the measures of two angles is 90°, then the angles are complementary.
m∠A + m∠B = 90°
Conclusion:
8. If the measure of an angle is between 90° and 180°, then the angle obtuse.
m∠A = 120°
Conclusion:
Use the Law of Syllogism to write the statement that follows from the pair of true statements.
9. If LK = 5 and MN = 5, then LK = MN.
If LK = MN, then LK ≅ MN
Conclusion:
10. If m∠A = 35° and m∠B = 55°, then m∠A + m∠B = 90°.
If the sum of the measures of two angles is 90°, then the angles are complementary.
Conclusion:
Answers: 3
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