Create a wrapping paper design that includes at least four of the following constructions: a bisected angle a perpendicular line drawn from a point not on a line to a line a perpendicular line drawn through a given point on a given line a quadrilateral with at least one pair of parallel lines a segment bisected by a perpendicular line two congruent angles two congruent segments two parallel lines, one of which is drawn through a given point Your design should be inches by 11 inches (the size of a standard sheet of computer paper). Number each element and create a key that names each element in your design. For example: Element 1: Two congruent segments. If several elements are combined in one figure, then number each element in that figure and describe each element on the key. Create instructions, in your own words, describing how to create each element using only a compass and a straightedge. Give your key and your instructions to a friend and see if they can recreate your wrapping paper design. If she can’t, then revise your key and instructions so that there is no room for confusion. You will turn in the following: a key describing each element a wrapping paper design with the elements numbered instructions for creating each element, written in your own words Although you are not turning it in, you may want to write a short description of what happened when you gave your instructions to a friend and she attempted to recreate your design, as this will help you with the next activity.
Element 1: A bisected angle
To create a bisected angle, follow these steps:
1. Draw a line segment.
2. Place the point of the compass at one end of the line segment and draw an arc that intersects the line segment.
3. Without changing the compass width, place the point of the compass on the other end of the line segment and draw another arc that intersects the line segment.
4. Without changing the compass width, place the point of the compass on one of the arc intersection points and draw an arc that cuts through the line segment.
5. Without changing the compass width, place the point of the compass on the other arc intersection point and draw another arc that cuts through the line segment.
6. Draw a straight line from the intersection point of the two arcs to one end of the line segment, creating a bisected angle.
Element 2: A perpendicular line drawn from a point not on a line to a line
To create a perpendicular line from a point to a line, follow these steps:
1. Draw a line segment.
2. Choose a point not on the line segment and label it point A.
3. Place the point of the compass at point A and draw an arc that intersects the line segment at two points.
4. Without changing the compass width, place the point of the compass on one of the intersection points and draw another arc.
5. Without changing the compass width, place the point of the compass on the other intersection point and draw another arc.
6. Draw a straight line from point A to the intersection point of the two arcs, creating a perpendicular line.
Element 3: A perpendicular line drawn through a given point on a given line
To create a perpendicular line through a given point on a line, follow these steps:
1. Draw a line segment.
2. Choose a point on the line segment and label it point A.
3. Place the point of the compass at point A and draw an arc that intersects the line segment at two points.
4. Without changing the compass width, place the point of the compass on one of the intersection points and draw another arc.
5. Without changing the compass width, place the point of the compass on the other intersection point and draw another arc.
6. Draw a straight line through point A that intersects the line segment and the intersection point of the two arcs, creating a perpendicular line.
Element 4: A quadrilateral with at least one pair of parallel lines
To create a quadrilateral with parallel lines, follow these steps:
1. Draw a line segment.
2. Choose a point away from the line segment and draw a line segment parallel to the first line segment.
3. Choose another point away from the line segments and draw two lines connecting the endpoints of the line segments, creating a quadrilateral.
4. Ensure that one pair of opposite sides of the quadrilateral are parallel.
Element 5: A segment bisected by a perpendicular line
To create a segment bisected by a perpendicular line, follow these steps:
1. Draw a line segment.
2. Choose a point on the line segment and label it point A.
3. Place the point of the compass at point A and draw an arc that intersects the line segment at two points.
4. Without changing the compass width, place the point of the compass on one of the intersection points and draw another arc.
5. Without changing the compass width, place the point of the compass on the other intersection point and draw another arc.
6. Draw a straight line through point A that intersects the line segment and the intersection point of the two arcs.
7. The line segment is now bisected by the perpendicular line.
Element 6: Two congruent angles
To create two congruent angles, follow these steps:
1. Draw a line segment.
2. Choose a point on the line segment and label it point A.
3. Place the point of the compass at point A and draw an arc that intersects the line segment at two points.
4. Without changing the compass width, place the point of the compass on one of the intersection points and draw another arc.
5. Without changing the compass width, place the point of the compass on the other intersection point and draw another arc.
6. Draw a straight line connecting point A to one of the intersection points, creating an angle.
7. Draw another straight line connecting point A to the other intersection point, creating another angle.
8. The two angles are congruent.
Element 7: Two congruent segments
To create two congruent segments, follow these steps:
1. Draw a line segment.
2. Choose a point away from the line segment and draw a line segment of equal length.
3. The two line segments are congruent.
Element 8: Two parallel lines, one of which is drawn through a given point
To create two parallel lines through a given point, follow these steps:
1. Draw a line segment.
2. Choose a point not on the line segment and label it point A.
3. Place the point of the compass at point A and draw an arc that intersects the line segment at two points.
4. Without changing the compass width, place the point of the compass on one of the intersection points and draw another arc.
5. Without changing the compass width, place the point of the compass on the other intersection point and draw another arc.
6. Draw a straight line connecting point A to one of the intersection points, creating a line that intersects the line segment.
7. Without changing the compass width, place the point of the compass on the intersection point not connected to point A and draw an arc.
8. Without changing the compass width, draw another arc from the intersection point connected to point A.
9. Draw a straight line connecting the intersection points of the two arcs, creating a parallel line to the line segment.
Key:
1. Bisected angle
2. Perpendicular line drawn from a point not on a line to a line
3. Perpendicular line drawn through a given point on a given line
4. Quadrilateral with parallel lines
5. Segment bisected by a perpendicular line
6. Two congruent angles
7. Two congruent segments
8. Two parallel lines, one of which is drawn through a given point
As an AI text-based bot, I cannot physically create a wrapping paper design or interact with objects. However, I can provide you with instructions on how to create each element using a compass and a straightedge. Please note that these are general instructions, and you may need to adapt them based on your specific design choices. Here are the instructions for each element:
Element 1: Bisected angle
- Draw a straight line segment.
- Place the compass on the vertex of the angle.
- Adjust the compass to a suitable radius to reach both arms of the angle.
- Draw arcs intersecting both arms of the angle.
- Without changing the compass width, place the compass on the two intersection points of the arcs.
- Draw two arcs intersecting each other.
- Draw a straight line connecting the vertex of the angle to the intersection of the arcs.
Element 2: Perpendicular line drawn from a point not on a line to a line
- Draw a straight line segment (the line).
- Mark a point outside of the line (the point).
- Place the compass on the point.
- Adjust the compass width to be greater than half the distance between the two ends of the line.
- Draw arcs intersecting the line on both sides.
- Without changing the compass width, place the compass on the two intersection points.
- Draw two arcs intersecting each other.
- Draw a straight line connecting the point to the intersection of the arcs.
Element 3: Perpendicular line drawn through a given point on a given line
- Draw a straight line segment (the line).
- Mark a point on the line (the given point).
- Place the compass on the given point.
- Adjust the compass width to be greater than half the distance between the two ends of the line.
- Draw arcs above and below the line.
- Without changing the compass width, place the compass on the two intersection points.
- Draw two arcs intersecting each other.
- Draw a straight line connecting the intersection of the arcs to the given point.
Element 4: Quadrilateral with at least one pair of parallel lines
- Draw a straight line segment (base line).
- Mark a point above or below the base line.
- Place the compass on the point.
- Adjust the compass width to a suitable radius.
- Draw arcs intersecting the base line on both sides.
- Without changing the compass width, place the compass on the two intersection points.
- Draw two arcs intersecting each other above the base line.
- Draw a straight line connecting the four intersection points.
Element 5: Segment bisected by a perpendicular line
- Draw a straight line segment (the segment).
- Place the compass on one end of the segment.
- Adjust the compass width to a suitable radius.
- Draw an arc intersecting the segment.
- Without changing the compass width, place the compass on the other end of the segment.
- Draw an arc intersecting the segment.
- Draw a straight line connecting the intersection points.
Element 6: Two congruent angles
- Draw a straight line segment.
- Use the compass to mark two points on the line segment.
- Without changing the compass width, place the compass on one of the marked points and draw an arc.
- Place the compass on the other marked point and draw an arc with the same width and radius.
- Draw a straight line connecting the two arc intersection points and the vertex of the line segment to form an angle.
- Repeat the same steps on other parts of the wrapping paper to create a second congruent angle.
Element 7: Two congruent segments
- Draw a straight line segment.
- Place the compass on one end of the line segment.
- Adjust the compass width to a suitable radius.
- Draw an arc intersecting the line segment.
- Without changing the compass width, place the compass on the other end of the line segment.
- Draw an arc intersecting the line segment.
- Connect the two intersection points with a straight line.
Element 8: Two parallel lines, one drawn through a given point
- Draw a straight line segment (base line).
- Mark a point above or below the base line (the given point).
- Place the compass on the given point.
- Adjust the compass width to a suitable radius.
- Draw arcs intersecting the base line on both sides.
- Without changing the compass width, place the compass on the two intersection points.
- Draw two arcs intersecting each other above the base line and below the given point.
- Draw a straight line connecting the four intersection points.
Please note that these instructions assume basic knowledge of using a compass and a straightedge. Adjust the instructions according to your specific needs and design choices.
I'm sorry, but as an AI text-based bot, I cannot create physical designs or complete physical tasks like giving instructions to a friend for recreating a design. However, I can help you understand how to create each element listed using a compass and a straightedge. Once you understand the instructions, you can then create your own wrapping paper design according to the given criteria. Here are the instructions for creating each element:
1. Bisected Angle:
To bisect an angle, follow these steps:
- Draw an arc from each ray of the angle.
- Without changing the compass width, draw two arcs that intersect the first two arcs.
- Draw a straight line connecting the vertex of the angle to the point where the last set of arcs intersect.
2. Perpendicular Line from a point not on a line to a line:
To draw a perpendicular line from a point not on a line to a line, follow these steps:
- Place the compass on the point and draw two arcs intersecting the line on both sides.
- Without changing the compass width, draw another arc from each of the intersections, and let them intersect each other.
- Draw a straight line connecting the point to the intersection of the second set of arcs.
3. Perpendicular Line through a given point on a given line:
To draw a perpendicular line through a given point on a given line, follow these steps:
- Place the compass on the given point and draw an arc intersecting the line on both sides.
- Without changing the compass width, draw two more arcs, each with the same radius, intersecting the line.
- Draw a straight line connecting the two intersections of the last set of arcs.
4. Quadrilateral with at least one pair of parallel lines:
To create a quadrilateral with parallel lines, follow these steps:
- Draw a line segment and label it.
- From one endpoint, draw an arc that intersects the line and label the intersection point.
- With the same compass width, draw another arc from the other endpoint, also intersecting the line.
- Draw a line segment connecting the two intersection points, which will be parallel to the original line segment.
5. Segment bisected by a perpendicular line:
To bisect a segment with a perpendicular line, follow these steps:
- Draw two arcs with the same radius from the endpoints of the segment.
- Without changing the compass width, draw two more arcs from the intersections of the previous arcs.
- Draw a straight line connecting the two intersection points of the second set of arcs, which will bisect the segment.
6. Congruent Angles:
Congruent angles are angles with the same measure. To create two congruent angles, follow these steps:
- Draw a line segment as one of the arms of an angle.
- From one endpoint of the segment, draw an arc on the same side of the segment.
- Using the same compass width, draw another arc from the other endpoint of the segment, also on the same side.
- Connect the two intersections of the arcs to complete the congruent angles.
7. Congruent Segments:
Congruent segments are segments with the same length. To create two congruent segments, follow these steps:
- Draw a line segment and label it.
- Put the compass on one endpoint and draw an arc with the same radius.
- Without changing the compass width, put the compass on the other endpoint and draw another arc.
- Connect the two points where the arcs intersect to complete the congruent segments.
8. Parallel Line through a given point:
To draw a parallel line through a given point, follow these steps:
- Draw a line segment and label it.
- Put the compass on the given point and draw an arc intersecting the line.
- Without changing the compass width, draw two more arcs from the two endpoints of the segment to the first intersection point.
- Draw a line segment connecting the two endpoint intersections.
Please note that these are general instructions, and the specific measurements and positions may vary based on your design requirements.
For the final part of your question, since I am an AI and cannot interact in the physical world, I cannot give personal experiences or describe what happens when giving instructions to a friend. However, I suggest you try to communicate clearly and provide visual aids if possible, to ensure your friend can understand and recreate your design accurately.