Questions: Using only your compass, straightedge, and a pencil, construct an angle congruent to of the following.

Solution Steps

Draw a ray \( DE \) on your paper. This will be one side of the new angle that will be congruent to \( \angle ABC \).

Place the compass point on vertex \( B \) of \( \angle ABC \) and draw an arc that intersects both sides of the angle. Label the points of intersection as \( F \) and \( G \).

Without changing the compass width, place the compass point on point \( D \) (the endpoint of the ray \( DE \)) and draw a similar arc that intersects the ray \( DE \). Label the intersection point as \( H \).

Place the compass point on point \( F \) and adjust the compass width to reach point \( G \).

Without changing the compass width, place the compass point on point \( H \) and draw an arc that intersects the previously drawn arc. Label the intersection point as \( I \).

Using the straightedge, draw a ray from point \( D \) through point \( I \). This ray \( DI \) forms the angle \( \angle EDI \) which is congruent to \( \angle ABC \).

Final Answer