Introduction to Proof Answers

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4 lines extend from point E. A horizontal line extends to the left to point A and a vertical line extends up to point C. Another line extends halfway between the other 2 lines to point B. Lines A E and E C form a right angle.

Question illustration
A
∠BEA ≅ ∠CEA
B
∠CEB ≅ ∠CEA
C
m∠CEB = 45°
D
m∠CEA = 45°
2
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A two-column proof

A
uses a visual representation of the logical flow of steps needed to reach a conclusion.
B
contains a table with a logical series of statements and reasons that reach a conclusion.
C
contains a set of sentences explaining the steps needed to reach a conclusion.
D
uses inductive reasoning to prove a statement.
3

The last line of a proof represents

A
the given information.
B
the argument.
C
the conclusion.
D
the assumptions.
4

Segment AB is congruent to segment AB.

A
reflexive
B
symmetric
C
transitive
D
substitution
5

4 lines are shown. One line contains points F, E, A. 3 lines come out of point E. One line goes to point D, another line goes to point B, and another line goes to point C. Angles B E C and B E A are congruent.

Question illustration
A
∠DEF is a right angle.
B
m∠DEA = m∠FEC
C
∠BEA ≅ ∠BEC
D
bisects ∠AEF.
Option D
6

A flow chart has 4 boxes. The top box is labeled given and contains angle A is-congruent-to angle B, angle C is congruent to angle B. The second box is labeled symmetric property and contains angle B is-congruent-to angle C. The third box is labeled question mark and contains angle A is congruent to angle C. The fourth box is labeled definition of congruent to angle x and contains m angle A = m angle C.

Question illustration
A
transitive property
B
reflexive property
C
symmetric property
D
substitution property
7

4 lines extend from point B. A line extends straight up from B to point A. Another line extends up and to the right to point C. Another line extends slight up and to the right to point D. The other line extends slightly down and to the right to point E.

Question illustration
A
∠ABC ≅ ∠ABD
B
∠ABD ≅ ∠CBE
C
∠CBD ≅ ∠DBE
D
∠CBD ≅ ∠ABC
8

A paragraph proof

A
uses inductive reasoning to prove a statement.
B
contains a table with a logical series of statements and reasons.
C
uses a visual chart of the logical flow of steps needed to reach a conclusion.
D
contains a set of sentences explaining the steps needed to reach a conclusion.
9

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

Question illustration
A
DB = BK
B
B is the midpoint of AC.
C
D bisects AK.
D
AK + BK = AC
10

Which are correct statements regarding proofs? Select three options.

A
In a paragraph proof, statements and their justifications are written in sentences in a logical order.
B
A two-column proof consists of a list statements and the reasons the statements are true.
C
A flowchart proof gives a visual representation of the sequence of steps without justifications.
D
A flowchart proof is a visual way of describing the statements and reasons for a proof.
E
A two-column proof lists only the given information and what is to be proven.

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