Question

using the compass and ruler, construct a congruent angle with vertex a. (to change the width of your compass, click on the compass button.)

Explanation:

Step1: Set compass width

Place the compass on the vertex of the given angle. Adjust the width to intersect both sides of the angle at two distinct points.

Step2: Transfer width to new vertex

Place the compass on vertex \(A'\) and draw an arc of the same radius as in Step1.

Step3: Measure chord length

Use the compass to measure the length of the chord formed by the intersection points on the given - angle's sides.

Step4: Mark point on new arc

With the same compass - width as in Step3, place the compass on the intersection of the arc and one of the rays starting from \(A'\) and draw an arc that intersects the previously drawn arc at a new point.

Step5: Draw new ray

Use the ruler to draw a ray from \(A'\) through the new intersection point. This forms an angle congruent to the given angle.

Answer:

The constructed angle with vertex \(A'\) is congruent to the given angle.