Introduction to Proofs

If m∠A = m∠B and m∠A + m∠C = m∠D, thenm∠B + m∠C = m∠D. Which property is shown?

• reflexive property

• substitution property

• symmetric property

• transitive property

Tags

CCSS.HSG.CO.C.10

CCSS.HSG.CO.C.9

What is the missing justification?

• transitive property

• reflexive property

• symmetric property

• substitution property

Tags

CCSS.HSA.REI.A.1

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 __________________ 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.HSG.CO.C.9

CCSS.HSG.CO.D.12

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.

Segment AB is congruent to segment AB. This statement shows the ______ property.

• reflexive

• symmetric

• transitive

• substitution

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.

Given that ∠CEA is a right angle and  EB bisects ∠CEA, which statement must be true?

• ∠BEA ≅ ∠CEA

• ∠CEB ≅ ∠CEA

• m∠CEB = 45°

• m∠CEA = 45°

Tags

CCSS.HSG.CO.C.9

Which statement is true about the diagram?

• K is the midpoint of AB.

• B is the midpoint of KT.

• AK = BT

• AB = KT

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.C.10

Which statement is true about the diagram?

• ∠DEF is a right angle.

• m∠DEA = m∠FEC

• ∠BEA ≅ ∠BEC

•  EB bisects ∠AEF.

Tags

CCSS.HSG.CO.C.9