Writing 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

Tags

CCSS.HSG.CO.C.10

CCSS.HSG.CO.C.9

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

What is the reason for the statement 2(3𝑚) − 2(5) = 8 in Step 2?

• Indirect proofs look for a contradiction to their original assumption, and

  direct proofs do not.

• Direct proofs use other theorems, rules, and definitions in their proofs, and

  indirect proofs do not.

• Indirect proof usually starts with the statement 'assume not' or 'assume the

  opposite', and direct proofs do not.

• Direct proofs involve assuming a hypothesis is true, and indirect proofs

  involve assuming a conjecture is false.

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

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

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Which of the following is NOT a difference between direct and indirect proofs?

• Indirect proofs look for a contradiction to their original assumption, and

  direct proofs do not.

• Direct proofs use other theorems, rules, and definitions in their proofs, and

  indirect proofs do not.

• Indirect proof usually starts with the statement 'assume not' or 'assume the

  opposite', and direct proofs do not.

• Direct proofs involve assuming a hypothesis is true, and indirect proofs

  involve assuming a conjecture is false.

Which statement is correct for Step 1 of the proof?

• 
• 
• 
• 

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

What is the reason for the statement 𝐴𝐵 = 𝐸𝐹 in Step 3 of the proof?

• Addition Property of Equality

• Distributive Property of Equality

• Subtraction Property of Equality

• Transitive Property of Equality

Tags

CCSS.HSA.REI.A.1

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.

Tags

CCSS.HSG.CO.C.10