Geometry 1-2 Complete Lesson: Points, Lines, and Planes

Solve It! Consider creating the figure shown with a pencil and a piece of paper. Is it possible with a straight arrow and a solid flat board? Explain.

Take Note: Describe the undefined term point. How are points named?

Take Note: Describe the undefined term line. How are lines named?

Take Note: Describe the undefined term plane. How are planes named?

Take Note: Define collinear in the response field.

On the canvas, sketch an example of a line, three collinear points and one non-collinear point. Name and label all four points.

Take Note: Define coplanar in the response field.

On the canvas, sketch an image that contains a plane, three coplanar points, and one non-coplanar point. Name and label the plane and all four points.

Problem 1 Got It?

Problem 1 Got It?
Select all that apply.

Problem 1 Got It?

Take Note: Define segment.

Sketch and label a segment on the canvas.

Take Note: Define ray.

Sketch and label a ray on the canvas.

Take Note: Define opposite rays.

Sketch and label a pair of opposite rays on the canvas.

Problem 2 Got It? Reasoning: Ray EF and ray FE form a line. Are they opposite rays? Explain. You may use the canvas to illustrate your explanation.

Take Note: What do we call the interstection of two distinct lines? Respond with one or two words.

Sketch two intersecting lines on the canvas. Label the lines and their intersection.

Take Note: What do we call the interstection of two distinct planes? Respond with one or two words.

Sketch two intersecting planes on the canvas. Label the planes and their intersection.

Problem 3 Got It? What are the names of two planes that intersect in line BF? Select both planes.

Problem 3 Got It? Reasoning: Why do you only need to find two common points to name the intersection of two distinct planes? You may use the canvas to illustrate your explanation.

Got It? Is it possible for three points to be non-coplanar?

Got It? Is it possible for four points to be non-coplanar?

Got It? Is it possible for four points to be coplanar?

Problem 4 Got It? What is the name of the plane that contains points L, M, and N? Shade the plane on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Problem 4 Got It? Reasoning: What is the name of a line that is coplanar with line JK and line KL?
Write your response in this format: line AB

Points Around the Room
Let the figure below model the math classroom. For perspective, assume that the door is between points F and A and that the teacher workstation is at about point k. Use the model to respond to the associated items.

The microwave is nearest to which point?

What object in the room is the closest to point F?

What do we usually call the object represented by plane FGK?

Vocabulary: A segment has endpoints R and S. What are two names for the segment?

Keep in mind that line segment names like those below will usually have small line segment symbols above them.

Reflect: Are ray AB and ray BA the same ray? Explain.

Keep in mind that ray names like these will usually have small ray symbols above them.

Reasoning: Why do you use two arrowheads when drawing or naming a line using two points?

Compare and Contrast: How is naming a ray similar to naming a line? How is it different?

Review Lesson 1-1: Make an orthographic drawing for the isometric drawing below.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Get Ready for Lesson 1-3: Simplify the absolute value. Enter only a number.

Algebra Review: Solve the equation. Show each step on the canvas.
You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Vocabulary Review: Match each net in the left column with the three-dimensional figure it represents on the right.

Vocabulary: Is the word conjecture used as a noun or verb in the sentence?

You make a conjecture that your volleyball team will win.

Vocabulary: Is the word conjecture used as a noun or verb in the sentence?

Assuming that your sister ate the last cookie is a conjecture.

Vocabulary: Is the word conjecture used as a noun or verb in the sentence?

You conjecture that your town will have an upgraded cellular tower.

Postulates: Complete the postulate.

Postulate 1-1 Through any two points there is exactly one __________.

Postulates: Complete the postulate.

Postulate 1-2 If two distinct lines intersect, then they intersect in exactly one __________.

Postulates: Complete the postulate.

Postulate 1-3 If two distinct planes intersect, then they intersect in exactly one __________.

Postulates: Complete the postulate.

Postulate 1-4 Through any three noncollinear points there is exactly one __________.

Reflection: Math Success

Solve It! Consider creating the figure shown with a pencil and a piece of paper. Is it possible with a straight arrow and a solid flat board? Explain.

Take Note: Describe the undefined term point. How are points named?

Take Note: Describe the undefined term line. How are lines named?

Take Note: Describe the undefined term plane. How are planes named?

Take Note: Define collinear in the response field. On the canvas, sketch an example of a line, three collinear points and one non-collinear point. Name and label all four points.

Take Note: Define coplanar in the response field. On the canvas, sketch an image that contains a plane, three coplanar points, and one non-coplanar point. Name and label the plane and all four points.

Problem 1 Got It?

Problem 1 Got It? Select all that apply.

Problem 1 Got It?

Problem 1 Got It?

Take Note: Define segment.Sketch and label a segment on the canvas.

Take Note: Define ray.Sketch and label a ray on the canvas.

Take Note: Define opposite rays.Sketch and label a pair of opposite rays on the canvas.

Problem 2 Got It? Reasoning: Ray EF and ray FE form a line. Are they opposite rays? Explain. You may use the canvas to illustrate your explanation.

Take Note: What do we call the interstection of two distinct lines? Respond with one or two words.Sketch two intersecting lines on the canvas. Label the lines and their intersection.

Take Note: What do we call the interstection of two distinct planes? Respond with one or two words.Sketch two intersecting planes on the canvas. Label the planes and their intersection.

Problem 3 Got It? What are the names of two planes that intersect in line BF? Select both planes.

Problem 3 Got It? Reasoning: Why do you only need to find two common points to name the intersection of two distinct planes? You may use the canvas to illustrate your explanation.

Got It? Is it possible for three points to be non-coplanar?

Got It? Is it possible for four points to be non-coplanar?

Got It? Is it possible for four points to be coplanar?

Problem 4 Got It? What is the name of the plane that contains points L, M, and N? Shade the plane on the canvas. You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Problem 4 Got It? Reasoning: What is the name of a line that is coplanar with line JK and line KL?Write your response in this format: line AB

The microwave is nearest to which point?

What object in the room is the closest to point F?

What do we usually call the object represented by plane FGK?

Vocabulary: A segment has endpoints R and S. What are two names for the segment? Keep in mind that line segment names like those below will usually have small line segment symbols above them.

Reflect: Are ray AB and ray BA the same ray? Explain.Keep in mind that ray names like these will usually have small ray symbols above them.

Reasoning: Why do you use two arrowheads when drawing or naming a line using two points?

Compare and Contrast: How is naming a ray similar to naming a line? How is it different?

Review Lesson 1-1: Make an orthographic drawing for the isometric drawing below. You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Get Ready for Lesson 1-3: Simplify the absolute value. Enter only a number.

Get Ready for Lesson 1-3: Simplify the absolute value. Enter only a number.

Algebra Review: Solve the equation. Show each step on the canvas. You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Vocabulary Review: Match each net in the left column with the three-dimensional figure it represents on the right.

Vocabulary: Is the word conjecture used as a noun or verb in the sentence?You make a conjecture that your volleyball team will win.

Vocabulary: Is the word conjecture used as a noun or verb in the sentence?Assuming that your sister ate the last cookie is a conjecture.

Vocabulary: Is the word conjecture used as a noun or verb in the sentence?You conjecture that your town will have an upgraded cellular tower.

Postulates: Complete the postulate.Postulate 1-1 Through any two points there is exactly one __________.

Postulates: Complete the postulate.Postulate 1-2 If two distinct lines intersect, then they intersect in exactly one __________.

Postulates: Complete the postulate.Postulate 1-3 If two distinct planes intersect, then they intersect in exactly one __________.

Postulates: Complete the postulate.Postulate 1-4 Through any three noncollinear points there is exactly one __________.

Reflection: Math Success

Take Note: Define collinear in the response field.

On the canvas, sketch an example of a line, three collinear points and one non-collinear point. Name and label all four points.

Take Note: Define coplanar in the response field.

On the canvas, sketch an image that contains a plane, three coplanar points, and one non-coplanar point. Name and label the plane and all four points.

Problem 1 Got It?
Select all that apply.

Take Note: Define segment.

Sketch and label a segment on the canvas.

Take Note: Define ray.

Sketch and label a ray on the canvas.

Take Note: Define opposite rays.

Sketch and label a pair of opposite rays on the canvas.

Take Note: What do we call the interstection of two distinct lines? Respond with one or two words.

Sketch two intersecting lines on the canvas. Label the lines and their intersection.

Take Note: What do we call the interstection of two distinct planes? Respond with one or two words.

Sketch two intersecting planes on the canvas. Label the planes and their intersection.

Problem 4 Got It? What is the name of the plane that contains points L, M, and N? Shade the plane on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Problem 4 Got It? Reasoning: What is the name of a line that is coplanar with line JK and line KL?
Write your response in this format: line AB

Vocabulary: A segment has endpoints R and S. What are two names for the segment?

Keep in mind that line segment names like those below will usually have small line segment symbols above them.

Reflect: Are ray AB and ray BA the same ray? Explain.

Keep in mind that ray names like these will usually have small ray symbols above them.

Review Lesson 1-1: Make an orthographic drawing for the isometric drawing below.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Algebra Review: Solve the equation. Show each step on the canvas.
You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Vocabulary: Is the word conjecture used as a noun or verb in the sentence?

You make a conjecture that your volleyball team will win.

Vocabulary: Is the word conjecture used as a noun or verb in the sentence?

Assuming that your sister ate the last cookie is a conjecture.

Vocabulary: Is the word conjecture used as a noun or verb in the sentence?

You conjecture that your town will have an upgraded cellular tower.

Postulates: Complete the postulate.

Postulate 1-1 Through any two points there is exactly one __________.

Postulates: Complete the postulate.

Postulate 1-2 If two distinct lines intersect, then they intersect in exactly one __________.

Postulates: Complete the postulate.

Postulate 1-3 If two distinct planes intersect, then they intersect in exactly one __________.

Postulates: Complete the postulate.

Postulate 1-4 Through any three noncollinear points there is exactly one __________.