GCA - Geometry A Introduction to Proof

Which are correct statements regarding proofs? Check all that apply.

RIGHT 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 paragraph proof is a two-column proof in sentence form. A flowchart proof includes a logical series of statements in boxes with connecting arrows.

Given: m∠AEB = 45° ∠AEC is a right angle. Prove: EB bisects ∠AEC. Proof: 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 EB divides ∠AEC into two congruent angles, it is the angle bisector.

RIGHT Angle Addition Postulate

Which statement is true about the given information?

RIGHT BD ≅ CE

Given that RT ≅ WX, which statement must be true?

RIGHT RT + TW = WX + TW

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

RIGHT Reflexive

A two-column proof

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

Given that BA bisects ∠DBC, which statement must be true?

RIGHT m∠ABD = m∠ABC

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

RIGHT m∠CEB = 45°

The last line of a proof represents

RIGHT the conclusion.

What is the missing justification? transitive property reflexive property symmetric property substitution property

RIGHT transitive property

Which statement is true about the diagram?

RIGHT ∠BEA ≅ ∠BEC