Introduction to Proof

Which statement is true about the diagram?

a. K is the midpoint of AB

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

a. m<ABD = m<ABC

What is the missing justification?

a. transitive property

Which statement is true about the given information?

c. BD ~= CE

The last line of a proof represents

c. the conclusion.

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

d. AK + BK = AC

A paragraph proof

d. contains a set of sentence explaining the steps needed to reach a conclusion.

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

In a paragraph proof, statements and their justifications are written in sentences in a logical order. A two-column proof consists of a list of statements and the reasons the statements are true. A paragraph proof id a two-column proof in sentence form. A flowchart proof includes a logical series of statements in boxes with connecting arrows.

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<AEC. Applying the substitution property gives 45°, so....

angle addition postulate

Given that <ABC ~= <DBE, which statement must be true?

b. <ABD ~= <CBE

A two-column proof

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

If m<A = M<B and m<A + m<C = <D, then m<B + m<C = <D. Which property is shown?

b. substitution property.

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

reflexive