Linear Pairs and Vertical Angles Answers

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1
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A horizontal line has points D, B, C. A line extends vertically from point B to point A.

Question illustration
A
m∠ABD = m∠ABC
B
AB ≅ BC
C
B is the midpoint of DC.
D
m∠DBC = 90°
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

Which statement is true about the given information?

Question illustration
A
BD = BC
Option A
B
BC = BE
Option B
C
BD ≅ CE
D
BC ≅ BD
4

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.

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.
5

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
6

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
7

Which statement is true about the diagram?

Question illustration
A
K is the midpoint of AB.
B
B is the midpoint of KT.
C
AK = BT
D
AB = KT
8

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
9

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.
10

segment addition propertyangle addition postulatereflexive propertytransitive property

A
segment addition property
B
angle addition postulate
C
reflexive property
D
transitive property

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