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Review of Geometry III

Review Test

Table of Contents

Further Reading

Given the following statements, what can you deduce? Every shop in town is closed. Every successful shop in town is an auto repair shop. Pavan's Auto Repair is a shop in town.

Given the following statements, what can you deduce? All new computers are fast. All cheetahs are fast. All cheetahs are mammals. Don is a cheetah with a new computer.

Given the following statements, what can you deduce? Everyone who lives on third street has a car. Everyone who owns a pet lives on third street. Susan owns a pet.

Given the following statements, what can you deduce? All squares are rhombuses. All rhombuses are parallelograms. All parallelograms are quadrilaterals. All quadrilaterals are polygons. Figure Q is a parallelogram.

Given the following statements, what can you deduce? If the stock market crashes, Tony's family will lose a lot of money. If a criminal robs the bank, Tony's family will lost a lot of money. Tony's family lost a lost of money.

>From which of the following groups of statements can the following be deduced? Jerry is a pilot.

Which of the following deductions is faulty?

Which of the following is a statement?

Which of the following is not a statement?

How is statement a related to statement p ? a : The ground is wet. p : The ground is not wet.

How is statement a related to statement p ? a : If it snows, Frank will go on a ski vacation. p : If it does not snow, Frank will not go on a ski vacation.

How is statement a related to statement d ? a : If Tony leaves, Ken will leave. d : If Ken does not leave, Tony will not leave.

Which of the following is the conjunction of statements p and q ? p : The grass is green. q : The flowers are blooming.

Which of the following statements is the implication of statements p and q , with p as the hypothesis and q as the conclusion? p : The book is published. q : The public will get angry.

Which of the following statements is the disjunction of statements p and q ? p : The blade is sharp. q : The material is strong.

How is statement a related to statements p and q ? a : The moon is bright and the star is dim. p : The moon is bright. q : The star is dim.

Given: p is true, q is true, and r is false. Which of the following statements has the same truth value as this statement: (pâá’q)âàèr .

Given: j is true, k is false, and l is false. Which of the following statements has the same truth value as this statement: (jâá’âàük)âàçâàül .

Given: s is false, t is false, u is false, and v is true. Which of the following statements has the same truth value as this statement: (sâàèv)âàç(vâá’u) .

Given: a is true, b is false, and c is true. Which of the following statements has the same truth value as this statement: (aâá’b)âá’c .

Given: (pâàçq) is true. Which of the following is also true?

If the conditional statement (pâá’q) is true, which of the following is always true?

If statements p and q are true, which of the following is also true?

What must be true of an implication that is true?

Given: p , q , and âàüs are all true. Which of the following is also true?

Given: the statement, (pâá’q)âàèq , is true. Which of the following always has a truth value of False?

The following are all examples of what? The reflexive property, the addition axiom, and the transitive property.

Which property tells us that a segment is congruent to itself?

Which property tells us that if two angles are congruent to a third angle, then they are congruent to each other?

Which property tells us that the union of supplementary angles is a straight angle?

If triangle ABC is congruent to triangle DEF, for what reason is segment BC congruent to segment EF?

What happens when a contradiction occurs?

If a median is drawn in a triangle, what can you deduce about the side to which the median is drawn?

What postulate allows for a perpendicular bisector to be drawn into a figure?

If segment AD is congruent to segment EC, and segment AB is congruent to segment AF, how do we know that AD + AB = EC + AF?

If segment BD is congruent to segment AE, and segment AE is congruent to segment EC, how do we know that segment BD is congruent to segment EC?

How do we know that angle BAF + angle FAC is equal to angle BAC?

If segment BA is congruent to segment FA, and segment EC is congruent to segment AD, how do we know that BA/EC = FA/AD?

If segment AF is congruent to segment AC, how do we know that AF - BD = AC - BD?

If segment BA is congruent to segment CA and segment DA is congruent to segment EA, how do we know that DA + EA = BA + CA?

Below is a direct proof with some reasons missing. What is the reason for statement 5?


Given:
Segment AC is congruent to segment AE.
Segment AD is perpendicular to segment BF.
Angle 1 is congruent to angle 2.
Prove:
Triangle ACF is congruent to triangle AEB.

Below is a direct proof with some reasons missing. What three numbers go in the parentheses in the reason for statement 7?


Given:
Segment AC is congruent to segment AE.
Segment AD is perpendicular to segment BF.
Angle 1 is congruent to angle 2.
Prove:
Triangle ACF is congruent to triangle AEB.

Below is a direct proof with some reasons missing. What is the correct reason for statement 8?


Given:
Segment AC is congruent to segment AE.
Segment AD is perpendicular to segment BF.
Angle 1 is congruent to angle 2.

Prove:
Triangle ACF is congruent to triangle AEB.

Below is a direct proof with some reasons missing. What is the correct reason for statement 11?


Given:
Segment AC is congruent to segment AE.
Segment AD is perpendicular to segment BF.
Angle 1 is congruent to angle 2.

Prove:
Triangle ACF is congruent to triangle AEB.

Below is a direct proof with some reasons missing. What is the correct reason for statements 12 and 13?


Given:
Segment AC is congruent to segment AE.
Segment AD is perpendicular to segment BF.
Angle 1 is congruent to angle 2.

Prove:
Triangle ACF is congruent to triangle AEB.

In the following direct proof, some reasons are missing. What is the correct reason for statement 2?


Given:
Triangle ABC is isosceles with vertex angle A.
Angle BDC is congruent to angle CEB.
Segment CD is a median
Segment BE is a median.
Prove:
Triangle BFC is isosceles.

In the following direct proof, some reasons are missing. What is the correct reason for statement 7?


Given:
Triangle ABC is isosceles with vertex angle A.
Angle BDC is congruent to angle CEB.
Segment CD is a median.
Segment BE is a median.
Prove:
Triangle BFC is isosceles.

In the following direct proof, some reasons are missing. What is the correct reason for statement 9?


Given:
Triangle ABC is isosceles with vertex angle A.
Angle BDC is congruent to angle CEB.
Segment CD is a median.
Segment BE is a median.
Prove:
Triangle BFC is isosceles.

In the following direct proof, some reasons are missing. What is the correct reason for statement 13?


Given:
Triangle ABC is isosceles with vertex angle A.
Angle BDC is congruent to angle CEB.
Segment CD is a median.
Segment BE is a median.
Prove:
Triangle BFC is isosceles.

In the following direct proof, some reasons are missing. What is the correct reason for statement 14?


Given:
Triangle ABC is isosceles with vertex angle A.
Angle BDC is congruent to angle CEB.
Segment CD is a median
Segment BE is a median.
Prove:
Triangle BFC is isosceles.

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