How to Construct an Angle Congruent to a Given Angle?
We have an angle ABC (Figure 2.7). We want to draw an angle equal to ABC. To do so, just follow the steps below. Figure 2.7 Step 1. Using a straightedge, draw a ray with any length you want (Figure 2.8). The lengths of the sides of any angles do not change the measure of the angle. Therefore, to draw a congruent of an angle you can choose any lengths for its sides. Figure 2.8 Step 2. Place the pointer of a compass at point B. Draw two arcs. These arcs must cut both sides of ABC. Name the crossing points of the arcs with the sides of ABC as E and F (Figure 2.9). Figure 2.9 Step 3. Dont change the compass setting you used in step 2. Place the pointer of the compass at M. Mark off an arc on (Figure 2.10). Label the crossing point of this arc with as D. Figure 2.10 Step 4. Put the pointer at F (Figure 2.11). Set the compass such that its pencil lies on point E. Figure 2.11 Step 5. Dont change the setting of the compass. Place the pointer at D. Then draw an arc such that it cuts arc DH at a
