HW #24 - Wayground - Proofs

Given: m∠AEB = 45° ∠AEC is a right angle.

Prove: EB bisects ∠AEC. Fill in the blank with the accurate property.

We are given that m∠AEB = 45° and ∠AEC is a right angle. The measure of ∠AEC is 90° by the definition of a right angle. Applying the (a)   gives m∠AEB + m∠BEC = m∠AEC. Applying the substitution property gives 45° + m∠BEC = 90°. The subtraction property can be used to find m∠BEC = 45°, so ∠BEC ≅ ∠AEB because they have the same measure. Since divides ∠AEC into two congruent angles, it is the angle bisector.

Tags

CCSS.8.G.A.5

Which are correct statements regarding proofs? Select three options.

• In a paragraph proof, statements and their justifications are written in sentences in a logical order. 

• A two-column proof consists of a list statements and the reasons the statements are true.

• A flowchart proof gives a visual representation of the sequence of steps without justifications.

• A flowchart proof is a visual way of describing the statements and reasons for a proof.

• A two-column proof lists only the given information and what is to be proven.

Tags

CCSS.HSG.CO.C.11

A paragraph proof

• uses inductive reasoning to prove a statement.

• contains a table with a logical series of statements and reasons.

• uses a visual chart of the logical flow of steps needed to reach a conclusion.

• contains a set of sentences explaining the steps needed to reach a conclusion.  

A two-column proof

• uses a visual representation of the logical flow of steps needed to reach a conclusion. 

• contains a table with a logical series of statements and reasons that reach a conclusion.

• contains a set of sentences explaining the steps needed to reach a conclusion.

• uses inductive reasoning to prove a statement.

Which statement is true about the diagram?

• ∠DEF is a right angle.

• m∠DEA = m∠FEC

• ∠BEA ≅ ∠BEC

•  EB bisects ∠AEF.

Tags

CCSS.7.G.B.5

Given that D is the midpoint of AB and K is the midpoint of BC, which statement must be true?

• DB = BK

• B is the midpoint of AC.

• D bisects AK.

• AK + BK = AC

Tags

CCSS.HSG.CO.C.10

The last line of a proof represents

• the given information.

• the argument.

• the conclusion.

• the assumptions.

When starting a proof you always start with:

• Given information
• What it wants you to prove
• Equal Angles
• Linear Angles

Tags

CCSS.8.G.A.5

Give the Reason for #1.

• Given

• Segment Addition Property

• Addition Property of Equality

• PQ + QR = PR

• Transitive Property of Equality

Tags

CCSS.HSG.SRT.B.5

Which property justifies step 2?

• Addition Property of Equality

• Subtraction Property of Equality

• Combine Like Terms

• Division Property of Equality

Tags

CCSS.HSA.REI.A.1