Explain how you can use 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, you will need a straightedge and a compass. Here are the steps to follow:
1. Begin by drawing a ray, which will serve as one side of your angle. This ray will be adjacent to the given angle.
2. Place the compass on the vertex of the given angle and adjust its width to any convenient length. This length will serve as the radius for the compass.
3. Keeping the compass at the same width, draw an arc from the vertex of the given angle across the ray that you drew in step 1. Label the point where the arc intersects the ray as point A.
4. Without changing the width of the compass, place its center on point A and draw another arc intersecting the ray. Label the point of intersection as point B.
5. Using the straightedge, draw a line segment connecting the vertex of the given angle to point B. This line segment will be the other side of the angle you are constructing.
Now, the angle you have constructed is both congruent (since it has the same measure) and adjacent (since it shares a common side) to the given angle.