Bisecting an angle
Draw ∠ABC = 70° with a protractor, with BC = BA = 5 cm, and bisect it.
Draw ∠ABC = 50° with a protractor, with BC = BA = 5.5 cm, and bisect it.
Draw ∠ABC = 60° with a protractor, with BC = BA = 5 cm, and bisect it.
Draw ∠ABC = 100° with a protractor, with BC = BA = 5 cm, and bisect it.
Draw ∠ABC = 140° with a protractor, with BC = BA = 4.5 cm, and bisect it.
1. Draw BC = 5 cm and, with a protractor, ∠ABC = 70°.
2. With B as the center and any radius, draw an arc that cuts BC at P and BA at Q.
3. With P as the center and a radius more than half of PQ, draw an arc inside the angle.
4. With Q as the center and the same radius, draw an arc that cuts it at R.
5. Join BR and produce it to D: BD bisects ∠ABC, so ∠ABD = ∠DBC = 35°.
1. Draw BC = 5.5 cm and, with a protractor, ∠ABC = 50°.
2. With B as the center and any radius, draw an arc that cuts BC at P and BA at Q.
3. With P as the center and a radius more than half of PQ, draw an arc inside the angle.
4. With Q as the center and the same radius, draw an arc that cuts it at R.
5. Join BR and produce it to D: BD bisects ∠ABC, so ∠ABD = ∠DBC = 25°.
1. Draw BC = 5 cm and, with a protractor, ∠ABC = 60°.
2. With B as the center and any radius, draw an arc that cuts BC at P and BA at Q.
3. With P as the center and a radius more than half of PQ, draw an arc inside the angle.
4. With Q as the center and the same radius, draw an arc that cuts it at R.
5. Join BR and produce it to D: BD bisects ∠ABC, so ∠ABD = ∠DBC = 30°.
1. Draw BC = 5 cm and, with a protractor, ∠ABC = 100°.
2. With B as the center and any radius, draw an arc that cuts BC at P and BA at Q.
3. With P as the center and a radius more than half of PQ, draw an arc inside the angle.
4. With Q as the center and the same radius, draw an arc that cuts it at R.
5. Join BR and produce it to D: BD bisects ∠ABC, so ∠ABD = ∠DBC = 50°.
1. Draw BC = 4.5 cm and, with a protractor, ∠ABC = 140°.
2. With B as the center and any radius, draw an arc that cuts BC at P and BA at Q.
3. With P as the center and a radius more than half of PQ, draw an arc inside the angle.
4. With Q as the center and the same radius, draw an arc that cuts it at R.
5. Join BR and produce it to D: BD bisects ∠ABC, so ∠ABD = ∠DBC = 70°.
Why it works
BP = BQ (one arc) and PR = QR (the same radius), and BR is common, so △BPR and △BQR are congruent (SSS). Their angles at B are equal: BR cuts ∠ABC in half.