Chapter 1 and 2 Geometry

Multiple Choice

Which of the following best describes a postulate in geometry?

• A statement that is proven using logic and reasoning

• A basic relationship assumed to be true without proof

• A mathematical formula used to solve equations

• A definition of a geometric shape

Open Ended

Why is it important to understand the foundations of geometry before studying more advanced topics in mathematics?

Multiple Choice

Which of the following statements is true according to the Expansion Postulate?

• A line contains at least three points.

• A plane contains at least two points.

• A plane contains at least three noncollinear points.

• Space contains at least three noncoplanar points.

Open Ended

Explain the relationship between points Q and S and the line α in the context of the Line Postulate.

Multiple Choice

Which of the following sets of points are noncollinear and lie in exactly one plane?

• Q, S, R

• Q, S, T

• Q, R, S

• P, Q, S

Fill in the Blank

If two points lie in a plane, then the line containing those two points lies in the same ___.

Open Ended

Describe what happens when two lines intersect, according to the Line Intersection Postulate.

Multiple Choice

If two planes intersect, what is the nature of their intersection according to the Plane Intersection Postulate?

• A single point

• A single line

• Two lines

• A plane

Multiple Choice

According to the Line Separation Postulate, how does a point on a line divide the line?

• Into two rays

• Into two half-lines and the point itself

• Into three equal segments

• Into two segments

Fill in the Blank

A segment consists of ___ points and all the points between them.

Multiple Choice

Which of the following statements about opposite rays is correct?

• They share the same endpoint and go in opposite directions.

• They are always parallel.

• They never intersect.

• They are the same as segments.

Open Ended

What is the difference between a half-line and a ray?

Open Ended

Explain how you would identify and name a ray and a segment using the points on the line in the last image.

Multiple Choice

Given the line with points C, X, R, A, T, and P, which of the following are correct ways to name a segment on this line?

• Segment XR

• Segment CT

• Segment XP

• All of the above

Multiple Choice

Which of the following best describes the geometric figure shown in the first image?

• A line with labeled points

• A ray with labeled points

• A line segment with labeled points

• A plane with labeled points

Fill in the Blank

The line that separates a plane into two half-planes is called the ___.

Open Ended

Explain the concept of a half-plane and how an edge divides a plane into two half-planes, using the diagrams provided.

Multiple Select

Which of the following statements are true about the plane separation postulate as shown in the images?

• Every line in a plane divides the plane into three disjoint sets.

• The three sets are the line itself and two half-planes.

• A plane can only be divided by a line into two sets.

• Opposite half-planes share a common edge.

Multiple Choice

Given the points E, F, G, and H on the line, what is the result of the intersection \( \overrightarrow{FG} \cap \overrightarrow{FE} \)?

• The point F

• The segment FG

• The entire line through F and G

• The segment FE

Open Ended

Describe how set operations such as union and intersection can be applied to subsets of lines and planes, using the given diagram and set notation.

Multiple Choice

Using the statements:
If it is Friday, then I will get paid.
It is Friday.
Write the conclusion.

• It is not Friday
• It is Friday
• I will not get paid
• I will get paid

Multiple Choice

How many cubes would be in the 10th figure?

• 18
• 16
• 17
• 41

Multiple Choice

What conclusion can be drawn from the following statements?
If the sun is shining, then it is a beautiful day.  
If it is a beautiful day, then we will have a picnic.

• If the sun is shining, then it is a beautiful day.
• If it is a beautiful day, then the sun is shining.
• If the sun is shining, then we will go on a picnic.
• If we go on a picnic, then the sun is shining.

Multiple Choice

What conclusion can be drawn from the following statements?
If the stereo is on, then the volume is loud.  
If the volume of the stereo is loud, then the neighbors will complain.

• If the neighbors complain, then the stereo will be loud.
• If the stereo is on, then the neighbors will complain.
• If the stereo is volume is loud, then the stereo is on.
• If the stereo is on, then the volume is loud.

Multiple Choice

How would you describe this pattern's rule?
65, 62, 59, 56, 53, 50

• Subtract 2
• Subtract 3
• Subtract 4
• Add 3

Multiple Choice

What are the missing numbers in this pattern?
12, 15, ___, 21, ____, 27

• 18,23
• 18, 24
• 17, 25
• 17, 24

Multiple Choice

Complete the conjecture.  Think of examples to help.
The product of any two odd numbers is _____________

• even
• odd
• zero
• positive

Multiple Choice

Complete the conjecture.  Think of examples to help.
The sum of an odd number and an even number is ________________

• even
• odd
• zero
• positive

Multiple Choice

Write the if-then statement that follows from the pair of true statements. If the sun is shining, then it is a beautiful day.  If it is a beautiful day, then we will have a picnic.

• If the sun is shining, then it is a beautiful day.
• If it is a beautiful day, then the sun is shining.
• If the sun is shining, then we will go on a picnic.
• If we go on a picnic, then the sun is shining.

Multiple Choice

What can be concluded from the following statements?
If Tom goes fishing then he brings a pole.
If Tom brings his pole then he catches a fish.

• If Tom goes fishing then he catches a fish.
• If Tom brings his pole then he goes fishing
•  If Tom catches a fish then he brought his pole.
• If Tom brings his pole then he catches a fish.

Multiple Choice

What can be concluded from the following statements?  
If Mike rakes leaves, then he bags them .
If Mike bags the leaves then he mows the lawn.

• If Mike mows the lawn then he bags the leaves.
• If Mike bags the leaves then he rakes.
• If Mike does not mow the lawn, then he did not rake the leaves.
• If Mike mows the lawn then he bags the leaves.

Multiple Choice

The type of reasoning where a person makes  conclusions based on observations and patterns is called...

• Inductive reasoning
• Deductive reasoning
• Conjecture
• Experiments

Multiple Choice

What is a conjecture?

• A statement believed to be true based on observations.
• An example which disproves an hypothesis.
• the performance of tricks that are seemingly magical

Multiple Choice

Which statement below is general?

• 14 is divisible by 7.

• Rhombus is a quadrilateral.

• All quadrilateral have four sides.

• The area of square is $$8\ mm^2$$ .

Multiple Choice

Inductive argument is a process of making a specific conclusion based on general premises.

• True

• False

Fill in the Blank

Determine the conclusion for each deductive argument to form a valid and sound deductive.

Premise 1 : All reptiles are cold blooded.

Premise 2 : Lizards are reptiles.

Conclusion : _____________________.

Multiple Choice

All women are mortal.

Gregoria De Jesus is a woman.

Therefore, Gregoria De Jesus is a mortal.

What kind of reasoning is shown in the given statements?

• Inductive

• Deductive

• Inductive and deductive

• No answer

Multiple Choice

Determine the next two terms of the sequence: 3, 7, 12, 18, _____.

• 23 and 32

• 30 and 20

• 25 and 33

• 19 and 28

Fill in the Blank

Filipinos are peace- loving people. Jose is a Filipino. Therefore______-

Multiple Choice

Which property justifies step 2?

• Addition Property of Equality

• Subtraction Property of Equality

• Combine Like Terms

• Division Property of Equality

Multiple Choice

Which property justifies step 3?

• Addition Property of Equality

• Subtraction Property of Equality

• Combine Like Terms

• Division Property of Equality

Multiple Choice

Which property justifies step 4?

• Addition Property of Equality

• Subtraction Property of Equality

• Combine Like Terms

• Division Property of Equality

Multiple Choice

Which property justifies step 5?

• Multiplication Property of Equality

• Subtraction Property of Equality

• Combine Constant Terms

• Division Property of Equality

Multiple Choice

Which property justifies step 6?

• Multiplication Property of Equality

• Subtraction Property of Equality

• Substitution Property of Equality

• Division Property of Equality

Multiple Choice

Name the property illustrated here.

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Multiple Choice

Name the property illustrated here.

• Reflexive Property of Equality

• Symmetric Property of Equality

• Transitive Property of Equality

• Division Property of Equality

Multiple Choice

Use the reflexive property to complete the statement.

• GH

• GH - GH

• GH + GH

• 2GH

Multiple Choice

Name the property of equality illustrated here.

• Reflexive Property

• Symmetric Property

• Transitive Property

• Distributive Property

Multiple Choice

Name the property of equality illustrated here.

• Reflexive Property

• Symmetric Property

• Transitive Property

• Distributive Property

Multiple Choice

Name the property of equality illustrated here.

• Addition Property of Equality

• Symmetric Property of Equality

• Transitive Property of Equality

• Distributive Property of Equality

Multiple Choice

Name the property of equality illustrated here.

• Addition Property of Equality

• Subtraction Property of Equality

• Combine Like Terms

• Distributive Property of Equality

Open Ended

How do postulates and theorems work together to build the foundations of geometry?

Multiple Choice

What is the main difference between a postulate and a theorem in geometry?

• A postulate is assumed true without proof, while a theorem is proven using logical reasoning.

• A postulate is proven using logical reasoning, while a theorem is assumed true without proof.

• Both postulates and theorems are assumed true without proof.

• Both postulates and theorems require experimental evidence.