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

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

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Solution Steps

Step 1: Draw a Ray

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

Step 2: Draw an Arc

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 \( G \).

Step 3: Copy the Arc

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 \( H \).

Step 4: Measure the Arc Distance

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

Step 5: Copy the Arc Distance

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 \( I \).

Step 6: Draw the Second Ray

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

The angle \( \angle EDI \) is congruent to \( \angle ABC \).

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