Direct and Indirect Proofs

What is a direct proof?

• A proof that always involves the multiplication of two values.

• A proof that can only use number properties to show that a certain

  statement is false.

• A proof that assumes a statement's hypothesis is true and uses a series of

  logical deductions to conclude that the statement's conclusion is true.

• A proof that assumes that the statement being proven is false and then

  attempts to find a contradiction to that assumption proving the original

  statement to be true.

Given ∠𝐴 ≅ ∠𝐵 and ∠𝐵 ≅ ∠𝐶. Prove ∠𝐴 ≅ ∠𝐶. What is the reason for the statement

𝑚∠𝐴 = 𝑚∠𝐶 in Step 3 of the proof?

• Addition Property of Equality

• Distributive Property of Equality

• Subtraction Property of Equality

• Transitive Property of Equality

Given ∠𝐴 is an angle. Prove ∠𝐴 ≅ ∠𝐴. What is the reason for the statement 𝑚∠𝐴 ≅

𝑚∠𝐴 in Step 2 of the proof?

• Distributive Property of Equality

• Reflexive Property of Equality

• Symmetric Property of Equality

• Transitive Property of Equality

What does an indirect proof rely on?

• a contradiction

• a function

• a product

• a sum

Which statement is true using Addition Property of Equality in Step 4?

• 6𝑚 − 10 − 8 = 8 − 8

• 6𝑚 − 10 + 8 = 8 + 8

• 6𝑚 − 10 + 10 = 8 + 10

• 6𝑚 − 10 − 10 = 8 − 10

What assumption would you make from the statement that, "There can be only one 90° angle in a triangle" using indirect proof?

• All the angles in a triangle add up to 90°.

• All the angles in a triangle add up to 180°.

• There can be more than one 90° angle in a triangle.

• There can be more than one 180° angle in a triangle.

What assumption would you make from the statement that “If 3𝑥 + 7 > 13, then

𝑥 > 2" using indirect proof?

• 𝑥 ≤ 2

• 𝑥 < 2

• 𝑥 ≥ 2

• 𝑥 = 2

What is the first step of an indirect proof?

• Write the given.

• Contradict the given.

• Assume the negation of the given.

• Assume the negation of what you are trying to prove.

If you were proving that a given line 𝑙, is perpendicular to another line 𝑗, using

indirect proof, what would your initial assumption be?

• Assume that line 𝑙 is not perpendicular to line 𝑗.

• Assume that line 𝑙 is perpendicular to line 𝑗.

• Assume that line 𝑙 and line 𝑗 are parallel.

• None of these are correct.

What is the “reason” for the "statement" 𝐵𝐶 = 𝐵𝐶 in Step 3 of the proof?

• Commutative Property

• Reflexive Property

• Symmetric Property

• Transitive Property