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Direct and Indirect Proofs

Authored by S S

Mathematics

9th Grade

CCSS covered

Used 15+ times

Direct and Indirect Proofs
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12 questions

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1.

MULTIPLE CHOICE QUESTION

2 mins • 2 pts

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.

2.

MULTIPLE CHOICE QUESTION

2 mins • 2 pts

Media Image

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.SRT.B.5

3.

MULTIPLE CHOICE QUESTION

2 mins • 2 pts

Media Image

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

Tags

CCSS.HSG.SRT.B.5

4.

MULTIPLE CHOICE QUESTION

2 mins • 2 pts

What does an indirect proof rely on?

a contradiction

a function

a product

a sum

5.

MULTIPLE CHOICE QUESTION

2 mins • 2 pts

Media Image

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

6.

MULTIPLE CHOICE QUESTION

2 mins • 2 pts

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.8.G.A.5

7.

MULTIPLE CHOICE QUESTION

2 mins • 2 pts

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

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