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: Draw a ray with vertex \(A'\)

Use the ruler to draw a ray starting from \(A'\).

Step2: Copy the arc of the original angle

Use the compass to measure the arc of the given angle (with the original vertex). Then, with the same compass width, draw an arc intersecting the ray at \(A'\).

Step3: Copy the second arc

Measure the arc that intersects the two sides of the original angle. With the same compass width, draw an arc from the intersection point on the ray at \(A'\) to intersect the first - drawn arc.

Step4: Draw the second side of the angle

Use the ruler to draw a ray from \(A'\) through the intersection point of the two arcs.

Answer:

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