Direct and Indirect Proof

Proof involving indirect reasoning. Also called proof by contradiction

• Direct reasoning

• Indirect reasoning

• Direct proof

• Indirect Proof

The first step of an indirect proof is to ____?

• write the given
• assume the negation of the given
• assume the negation of what you are trying to prove
• contradict the given

The second step of an indirect proof is to ____?

• assume the negation of the given

• assume the negation of what you are trying to prove

• conclude the prove is true

• contradict the given using logical statements based on the initial assumption

What assumption would you make to start the indirect proof of ∆ABC≅∆DEF?

• ∆ABC≠∆DEF
• ∆ABC≇∆DEF
• <ABC≠<DEF
• AB≅DE

Tags

CCSS.HSG.SRT.B.5

What assumption would you make to start the indirect proof of AB≅BC?

• AB≠BC
• BA≅CB
• B is the midpoint of AC
• B is the perpendicular bisector oa AC

Tags

CCSS.HSG.CO.C.9

What assumption would you make to start the indirect proof of:
 there can be only one 90 angle in a triangle

• there can be more than one 90 angle in a triangle
• <a+<b+<c=180
• <a+<b+<c≠180
• all the angles in a triangle add up to 180.

Tags

CCSS.8.G.A.5

Which statement is a contradiction of the statement XY≅RT?

• XY<RT
• TR≅YX
• XY≈RT
• XY≤RT

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

What assumption would you make to start the indirect proof of if 3x+7>13, then x>2?

• x≤2
• x<2
• x>2
• x=2

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

A way to reach a conclusion using reasoning:

• Proof

• hypothesis

• counterexample

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.11

CCSS.HSA.SSE.A.2

A proof that can be used when there are only two possibilities; if one possibility is false, the other must be true.

• direct proof

• indirect proof

• conclusion