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
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.
1 answer