Title: (Canvas-Quiz)G02_Starting Geometric Proofs
Course: HBUHSD Geometry Resource Course > Section: Unit 1: Foundational Geometric Concepts

Q: Based on the pattern, what are the next two terms of the sequence?
9, 15, 21, 27, . . .
- 33, 972
- 39, 45
- 162, 972
- 33, 39
A: 33, 39

Q: Based on the pattern, what are the next two terms of the sequence?
, . . .
A: (a choice with no text)

Q: Based on the pattern, what is the next figure in the sequence?
A: (a choice with no text)

Q: What conjecture can you make about the fourteenth figure in this pattern?
- The fourteenth figure in the pattern is.
- The fourteenth figure in the pattern is.
- The fourteenth figure in the pattern is.
- There is not enough information.
A: The fourteenth figure in the pattern is.

Q: What conjecture can you make about the twentieth term in the pattern A, B, A, C, A, B, A, C?
- The twentieth term is C.
- The twentieth term is A.
- The twentieth term is B.
- There is not enough information.
A: The twentieth term is C.

Q: What conjecture can you make about the sum of the first 10 odd numbers?
- The sum is .
- The sum is .
- The sum is .
- The sum is .
A: The sum is .

Q: What conjecture can you make about the sum of the first 40 positive even numbers?

2 | = | 2 | = |
2 + 4 | = | 6 | = |
2 + 4 + 6 | = | 12 | = |
2 + 4 + 6 + 8 | = | 20 | = |
2 + 4 + 6 + 8 + 10 | = | 30 | = |
- The sum is .
- The sum is .
- The sum is .
- The sum is .
A: The sum is .

Q: What conjecture can you make about the product of 13 and 8,888,888?

88 | = | 1144
888 | = | 11,544
8888 | = | 115,544
88,888 | = | 1,155,544
- 115,555,544
- 1,115,555,444
- 1,155,555,544
- 11,155,555,444
A: 115,555,544

Q: Alfred is practicing typing. The first time he tested himself, he could type 45 words per minute. After practicing for a week, he could type 48 words per minute. After two weeks he could type 51 words per minute. Based on this pattern, predict how fast Alfred will be able to type after 4 weeks of practice.
- 61 words per minute
- 57 words per minute
- 54 words per minute
- 51 words per minute
A: 57 words per minute

Q: Laisha’s Internet Services designs web sites and recently began a weekly advertising campaign. Laisha noticed an increase in her customers over a period of five consecutive weeks. Based on the pattern shown in the graph, make a conjecture about the number of customers Laisha will have in the seventh week.
- Laisha will have 7 customers.
- Laisha will have 9 customers.
- Laisha will have 11 customers.
- Laisha will have 13 customers.
A: Laisha will have 13 customers.

Q: What is a counterexample for the conjecture?
Conjecture: The product of two positive numbers is greater than the sum of the two numbers.
- 3 and 5
- 2 and 2
- A counterexample exists, but it is not shown above.
- There is no counterexample. The conjecture is true.
A: 2 and 2

Q: What is a counterexample for the conjecture?
Conjecture: Any number that is divisible by 4 is also divisible by 8.
- 24
- 40
- 12
- 26
A: 12

Q: What is the conclusion of the following conditional?
A number is divisible by 2 if the number is even.
- The sum of the digits of the number is divisible by 2.
- If a number is even, then the number is divisible by 2.
- The number is even.
- The number is divisible by 2.
A: The number is divisible by 2.

Q: Identify the hypothesis and conclusion of this conditional statement:
If two lines intersect at right angles, then the two lines are perpendicular.
- Hypothesis: The two lines are perpendicular.
Conclusion: Two lines intersect at right angles.
- Hypothesis: Two lines intersect at right angles.
Conclusion: The two lines are perpendicular.
- Hypothesis: The two lines are not perpendicular.
Conclusion: Two lines intersect at right angles.
- Hypothesis: Two lines intersect at right angles.
Conclusion: The two lines are not perpendicular.
A: Hypothesis: Two lines intersect at right angles.
Conclusion: The two lines are perpendicular.

Q: Which choice shows a true conditional, with the hypothesis and conclusion identified correctly?
- Yesterday was Monday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was Monday.
- If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is not Thursday.
- If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is Thursday.
- Yesterday was Tuesday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was Tuesday.
A: Yesterday was Tuesday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was Tuesday.

Q: Another name for an if-then statement is a ____. Every conditional has two parts. The part following if is the ____ , and the part following then is the ____.
- conditional; conclusion; hypothesis
- hypothesis; conclusion; conditional
- conditional; hypothesis; conclusion
- hypothesis; conditional; conclusion
A: conditional; hypothesis; conclusion

Q: Write this statement as a conditional in if-then form:
All triangles have three sides.
- If a triangle has three sides, then all triangles have three sides.
- If a figure has three sides, then it is not a triangle.
- If a figure is a triangle, then all triangles have three sides.
- If a figure is a triangle, then it has three sides.
A: If a figure is a triangle, then it has three sides.

Q: Draw a Venn diagram to illustrate this conditional:
Cars are motor vehicles.
A: (a choice with no text)

Q: A conditional can have a ____ of true or false.
- hypothesis
- truth value
- counterexample
- conclusion
A: truth value

Q: Which statement is a counterexample for the following conditional?
If you live in Springfield, then you live in Illinois.
- Sara Lucas lives in Springfield.
- Jonah Lincoln lives in Springfield, Illinois.
- Billy Jones lives in Chicago, Illinois.
- Erin Naismith lives in Springfield, Massachusetts.
A: Erin Naismith lives in Springfield, Massachusetts.

Q: What is the converse of the following conditional?
If a point is in the fourth quadrant, then its coordinates are negative.
- If a point is in the fourth quadrant, then its coordinates are negative.
- If a point is not in the fourth quadrant, then the coordinates of the point are not negative.
- If the coordinates of a point are not negative, then the point is not in the fourth quadrant.
- If the coordinates of a point are negative, then the point is in the fourth quadrant.
A: If the coordinates of a point are negative, then the point is in the fourth quadrant.

Q: Which conditional has the same truth value as its converse?
- If x = 7, then .
- If a figure is a square, then it has four sides.
- If x – 17 = 4, then x = 21.
- If an angle has a measure of 80, then it is acute.
A: If x – 17 = 4, then x = 21.

Q: For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.
If x = 7, then x^2 = 49.
- If x^2 = 49, then x = 7. True; x^2 = 49 if and only if x = 7.
- If x^2 = 49, then x = 7. True; x = 7 if and only if x^2 = 49.
- If x^2 = 49, then x = 7. False
- If x^2 = 7, then x = 49. False
A: If x^2 = 49, then x = 7. False

Q: What is the converse of the following true conditional? If the converse is true, rewrite the statements as a biconditional. If either is false, give a counterexample.
If two lines are parallel, they do not intersect.
- If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.
- If two lines do not intersect, they are parallel. One statement is false. If two lines are parallel, they may intersect twice.
- If two lines do not intersect, they are parallel. Both statements are true. Two lines are parallel if (and only if) they do not intersect.
- If two lines do not intersect, they are not parallel. Both statements are true. Two lines are not parallel if (and only if) they do not intersect.
A: If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.

Q: When a conditional and its converse are true, you can combine them as a true ____.
- counterexample
- biconditional
- unconditional
- hypothesis
A: biconditional

Q: Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample.
If an angle is a right angle, its measure is 90.
If an angle measure is 90, the angle is a right angle.
- One statement is false. If an angle measure is 90, the angle may be a vertical angle.
- One statement is false. If an angle is a right angle, its measure may be 180.
- Both statements are true. An angle is a right angle if (and only if) its measure is 90.
- Both statements are true. The measure of angle is 90 if (and only if) it is not a right angle.
A: Both statements are true. An angle is a right angle if (and only if) its measure is 90.

Q: Write the two conditional statements that make up the following biconditional.
I drink juice if (and only if) it is breakfast time.
- I drink juice if (and only if) it is breakfast time.
It is breakfast time if (and only if) I drink juice.
- If I drink juice, then it is breakfast time.
If it is breakfast time, then I drink juice.
- If I drink juice, then it is breakfast time.
I drink juice only if it is breakfast time.
- I drink juice.
It is breakfast time.
A: If I drink juice, then it is breakfast time.
If it is breakfast time, then I drink juice.

Q: Is the following definition of dog reversible? If yes, write it as a true biconditional.
A dog is a mammal.
- The reverse is false.
- The reverse is true. An animal is a dog if (and only if) it is a mammal.
- The reverse is true. An animal is a mammal if (and only if) it is a dog.
- The reverse is true. If an animal is a dog, then it is a mammal.
A: The reverse is false.

Q: Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.
Two lines that intersect at right angles are perpendicular.
- The statement is not reversible.
- Yes; if two lines intersect at right angles, then they are perpendicular.
- Yes; if two lines are perpendicular, then they intersect at right angles.
- Yes; two lines intersect at right angles if (and only if) they are perpendicular.
A: Yes; two lines intersect at right angles if (and only if) they are perpendicular.

Q: Is the statement a good definition? If not, find a counterexample.
A square is a figure with two pairs of parallel sides and four right angles.
- The statement is a good definition.
- No; a rhombus is a counterexample.
- No; a rectangle is a counterexample.
- No; a parallelogram is a counterexample.
A: No; a rectangle is a counterexample.

Q: One way to show that a statement is NOT a good definition is to find a ____.
- converse
- conditional
- biconditional
- counterexample
A: counterexample

Q: Which statement provides a counterexample to the following faulty definition?
A square is a figure with four congruent sides.
- A six-sided figure can have four sides congruent.
- Some triangles have all sides congruent.
- A square has four congruent angles.
- A rectangle has four sides.
A: A six-sided figure can have four sides congruent.

Q: Which biconditional is NOT a good definition?
- A whole number is even if and only if it is divisible by 2.
- A whole number is odd if and only if the number is not divisible by 2.
- An angle is straight if and only if its measure is 180.
- A ray is a bisector of an angle if and only if it splits the angle into two angles.
A: A ray is a bisector of an angle if and only if it splits the angle into two angles.

Q: Which statement is the Law of Detachment?
- If is a true statement and q is true, then p is true.
- If is a true statement and q is true, then is true.
- If and are true, then is a true statement.
- If is a true statement and p is true, then q is true.
A: If is a true statement and p is true, then q is true.

Q: If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.
Statement 1: If x = 7, then 7x – 2 = 47.
Statement 2: x = 7
- x = 7
- If 7x – 2 = 47, then x = 7.
- 7x – 2 = 47
- not possible
A: 7x – 2 = 47

Q: Use the Law of Detachment to draw a conclusion from the two given statements.
If two angles are complementary, then the sum of their measures is 90°.
and are complementary.
- + = 180
- is congruent to .
- + = 90
A: + = 90

Q: Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.
I can go to the concert if I can afford to buy a ticket.
I can go to the concert.
- I can afford to buy a ticket.
- I cannot afford to buy the ticket.
- If I can go to the concert, I can afford the ticket.
- not possible
A: not possible

Q: Use the Law of Syllogism to draw a conclusion from the two given statements.
If you exercise regularly, then you have a healthy body.
If you have a healthy body, then you have more energy.
- If you do not have more energy, then you do not exercise regularly.
- You have more energy.
- You have a healthy body.
- If you exercise regularly, then you have more energy.
A: If you exercise regularly, then you have more energy.

Q: Which statement is the Law of Syllogism?
- If is a true statement and p is true, then q is true.
- If is a true statement and q is true, then p is true.
- If and are true statements, then is a true statement.
- If and are true statements, then is a true statement.
A: If and are true statements, then is a true statement.

Q: Use the Law of Syllogism to draw a conclusion from the two given statements.
If two lines intersect and form right angles, then the lines are perpendicular.
If two lines are perpendicular, then they intersect and form 90° angles.
- The lines are perpendicular.
- If two lines intersect and form right angles, then they intersect and form 90° angles.
- The lines intersect and form 90° angles.
- If two lines do not intersect and form 90° angles, then they do not form right angles.
A: If two lines intersect and form right angles, then they intersect and form 90° angles.

Q: Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements.
If it is Friday night, then there is a football game.
If there is a football game, then Josef is wearing his school colors.
It is Friday night.
- If it is Friday night, then Josef is wearing his school colors.
- Josef is wearing his school colors.
- There is a football game.
- If it is not Friday night, then Josef is not wearing his school colors.
A: Josef is wearing his school colors.

Q: Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements.
If an elephant weighs more than 2000 pounds, then it weighs more than Jill’s car.
If something weighs more than Jill’s car, then it is too heavy for the bridge.
Smiley the elephant weighs 2150 pounds.
- Smiley is too heavy for the bridge.
- Smiley weighs more than Jill’s car.
- If Smiley weighs more than 2000 pounds, then Smiley is too heavy for the bridge.
- If Smiley weighs more than Jill’s car, then Smiley is too heavy for the bridge.
A: Smiley is too heavy for the bridge.

Q: What is the value of x? Identify the missing justifications.
, , and .

 |  | a. __________
x – 5 + x – 7 = 100 |  | b. Substitution Property
2x – 12 = 100 |  | c. Simplify
2x = 112 |  | d. __________
x = 56 |  | e. Division Property of Equality
- Angle Addition Postulate; Subtraction Property of Equality
- Angle Addition Postulate; Addition Property of Equality
- Protractor Postulate; Addition Property of Equality
- Protractor Postulate; Subtraction Property of Equality
A: Angle Addition Postulate; Addition Property of Equality

Q: bisects = 7x. = . Find
- 108
- 72
- 180
- 252
A: 252

Q: Name the Property of Equality that justifies this statement:
If l = m, then .
- Multiplication Property
- Symmetric Property
- Subtraction Property
- Transitive Property
A: Symmetric Property

Q: Which statement is an example of the Addition Property of Equality?
- If p = q then .
- If p = q then .
- If p = q then .
- p = q
A: If p = q then .

Q: Use the given property to complete the statement.

Transitive Property of Congruence
If ______.
A: (a choice with no text)

Q: Use the given property to complete the statement.

Multiplication Property of Equality
If , then ______.
A: (a choice with no text)

Q: Use the given property to complete the statement.

Substitution Property of Equality
If , then ______.
A: (a choice with no text)

Q: Name the Property of Congruence that justifies the statement:
If .
- Symmetric Property
- Transitive Property
- Reflexive Property
- none of these
A: Symmetric Property

Q: Name the Property of Congruence that justifies this statement:
If .
- Transitive Property
- Symmetric Property
- Reflexive Property
- none of these
A: Transitive Property

Q: Complete the two-column proof.
Given:
Prove:
- a. Given
b. Substitution Property
c. Addition Property of Equality
d. Division Property of Equality
e. Symmetric Property of Equality
- a. Given
b. Substitution Property
c. Addition Property of Equality
d. Addition Property of Equality
e. Symmetric Property of Equality
- a. Given
b. Symmetric Property of Equality
c. Addition Property of Equality
d. Division Property of Equality
e. Reflexive Property of Equality
- a. Given
b. Substitution Property
c. Addition Property of Equality
d. Division Property of Equality
e. Reflexive Property of Equality
A: a. Given
b. Substitution Property
c. Addition Property of Equality
d. Division Property of Equality
e. Symmetric Property of Equality

Q: Complete the two-column proof.
Given:
Prove:
- a. Given
b. Subtraction Property of Equality
c. Division Property of Equality
- a. Given
b. Subtraction Property of Equality
c. Multiplication Property of Equality
- a. Given
b. Addition Property of Equality
c. Multiplication Property of Equality
- a. Given
b. Addition Property of Equality
c. Division Property of Equality
A: a. Given
b. Subtraction Property of Equality
c. Multiplication Property of Equality

Q: What is the value of x?
- –16
- 120
- 60
- 16
A: 16

Q: What is the value of x?
- 84
- 36
- 120
- 60
A: 60

Q: Find
- 150
- 30
- 160
- 20
A: 30

Q: Find the values of x and y.
- x = 15, y = 17
- x = 112, y = 68
- x = 68, y = 112
- x = 17, y = 15
A: x = 15, y = 17

Q: What is the converse and the truth value of the converse of the following conditional?
If an angle is a right angle, then its measure is 90.
- If an angle is not a right angle, then its measure is 90.
False
- If an angle is not a right angle, then its measure is not 90.
True
- If an angle has a measure of 90, then it is a right angle.
False
- If an angle has a measure of 90, then it is a right angle.
True
A: If an angle has a measure of 90, then it is a right angle.
True