Explain how you can use a straightedge and a compass to construct an angle that is both
congruent and adjacent to a given angle.
(1 point
To construct an angle that is both congruent and adjacent to a given angle using a straightedge and a compass, follow these steps:
1. Draw a line segment and label one endpoint as point A.
2. Place the compass point on point A and draw an arc that intersects the line segment.
3. Without changing the compass width, place the compass point on the intersection of the arc and the line segment and draw another arc above the line segment.
4. Without changing the compass width, place the compass point on the intersection of the arc and the line segment and draw another arc below the line segment.
5. Using the straightedge, draw a line through point A and the intersection point of the lower arc and the line segment. This line will represent the given angle.
6. Place the compass point on the intersection of the upper arc and the line segment and draw a new arc above the line segment.
7. Without changing the compass width, place the compass point on the intersection of the new arc and the line segment and draw another arc below the line segment.
8. Using the straightedge, draw a line through point A and the intersection point of the lower arc and the line segment. This line will be the constructed angle that is congruent and adjacent to the given angle.
By following these steps, you have used a straightedge and a compass to construct an angle that is both congruent and adjacent to a given angle.
To construct an angle that is both congruent and adjacent to a given angle using a straightedge and compass, follow these steps:
1. Place the straightedge so that one of its ends is touching the vertex of the given angle.
2. Draw a line segment using the straightedge, extending it from the vertex of the given angle.
3. With the compass, place the needle on the vertex of the given angle and adjust its width to any convenient length.
4. Using the compass, draw an arc on the line segment previously drawn, starting from one of the points where the line segment intersects the given angle.
5. Without changing the width of the compass, place the needle on the other intersection point where the line segment meets the given angle.
6. Draw another arc that intersects the previous arc on the line segment.
7. Using the straightedge, draw a line connecting the vertex of the given angle and the point of intersection between the two arcs on the line segment.
8. The angle formed by the line connecting the vertex and the point of intersection is congruent and adjacent to the given angle.
By following these steps, you can construct an angle that is both congruent and adjacent to a given angle using just a straightedge and compass.
To construct an angle that is both congruent and adjacent to a given angle, you can use a straightedge and a compass. Here are the steps to follow:
1. Start by drawing the given angle using a straightedge. Label the vertex of the angle as point A, and the two rays forming the angle as AB and AC.
2. Take your compass and place the sharp end on point A. Open the compass to any convenient width, and draw an arc that intersects both rays AB and AC.
3. Without changing the width of the compass, place the sharp end on the point where the arc intersects ray AB, and draw another arc inside the angle.
4. Repeat the previous step, but this time place the sharp end on the point where the arc intersects ray AC, and draw another arc inside the angle.
5. Take your straightedge and draw a line from the vertex A to the point where the two smaller arcs intersect. This line will be congruent to the given angle and also adjacent to it.
Now you have successfully constructed an angle that is both congruent and adjacent to the given angle using a straightedge and a compass.