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, you can use a straightedge and a compass in the following steps:
1. Start by drawing a line segment, which will serve as the base for the given angle.
2. Place the compass on one endpoint of the base and draw an arc that intersects the base line.
3. Without changing the compass width, place the compass on the other endpoint of the base and draw another arc that intersects the base line.
4. Using the straightedge, draw a line connecting the intersection points of the two arcs and the base line. This line will be congruent to the given angle.
5. To make the constructed angle adjacent to the given angle, extend the line you just drew beyond the intersection point with the base line.
Now, you have successfully constructed an angle that is both congruent and adjacent to the given angle using a straightedge and a compass.
To construct an angle that is both congruent and adjacent to a given angle using a straightedge and a compass, follow these steps:
1. Start by drawing a line and labeling it as the given angle. This will serve as one side of the angle you want to construct.
2. Place the pointed end of the compass at the vertex of the given angle, and draw an arc that intersects the sides of the angle.
3. Without changing the compass width, move the compass so that the pointed end is now placed at one of the points where the arc intersects the side of the given angle. Draw another arc that intersects the side of the given angle.
4. Without changing the compass width, move the compass so that the pointed end is now placed on the other point where the second arc intersects the side of the given angle. Draw a third arc that intersects both previous arcs.
5. Use the straightedge to connect the vertex of the given angle with the point of intersection of the two smaller arcs. This line will be the second side of the constructed angle.
6. Finally, draw a ray extending from the vertex of the given angle on the opposite side from the constructed angle. This will complete the construction of the angle that is congruent and adjacent to the given angle.