A triangle equal to a triangle
Construct △ABC with BC = 4.4 cm, ∠ABC = 60° and AB = 5.5 cm. Then construct △DBC of the same area with ∠BCD = 120°.
Construct △ABC with BC = 4.4 cm, ∠ABC = 60° and AB = 5.5 cm. Then construct △DBC of the same area with DB = 6.2 cm.
Construct △ABC with BC = 6.4 cm, AB = 5.6 cm and AC = 6 cm. Then construct △DBC of the same area with DB = 7 cm.
Construct △ABC with BC = 5 cm, ∠ABC = 45° and AB = 6 cm. Then construct △DBC of the same area right-angled at C.
Construct △ABC with BC = 5 cm, ∠ABC = 45° and ∠ACB = 60°. Then construct △DBC of the same area with DB = 6.5 cm.
1. Draw BC = 4.4 cm.
2. At B, construct ∠ABC = 60° and cut BA = 5.5 cm on its arm. Join AC.
3. Through A, draw ST ∥ BC by copying ∠ABC at A, so that ∠BAS = ∠ABC (alternate angles).
4. At C, construct ∠BCD = 120°; its arm meets ST at D.
5. Join DB: △DBC has the same area as △ABC.
1. Draw BC = 4.4 cm.
2. At B, construct ∠ABC = 60° and cut BA = 5.5 cm on its arm. Join AC.
3. Through A, draw ST ∥ BC by copying ∠ABC at A, so that ∠BAS = ∠ABC (alternate angles).
4. With B as the center and radius 6.2 cm, cut ST at D.
5. Join DB and DC: △DBC has the same area as △ABC.
1. Draw BC = 6.4 cm.
2. With B as the center and radius 5.6 cm, and C as the center and radius 6 cm, draw arcs that cut at A. Join AB and AC.
3. Through A, draw ST ∥ BC by copying ∠ABC at A, so that ∠BAS = ∠ABC (alternate angles).
4. With B as the center and radius 7 cm, cut ST at D.
5. Join DB and DC: △DBC has the same area as △ABC.
1. Draw BC = 5 cm.
2. At B, construct ∠ABC = 45° and cut BA = 6 cm on its arm. Join AC.
3. Through A, draw ST ∥ BC by copying ∠ABC at A, so that ∠BAS = ∠ABC (alternate angles).
4. At C, construct ∠BCD = 90°; its arm meets ST at D.
5. Join DB: △DBC has the same area as △ABC.
1. Draw BC = 5 cm.
2. At B, construct an angle of 45°, and at C an angle of 60°. Their arms meet at A.
3. Through A, draw ST ∥ BC by copying ∠ABC at A, so that ∠BAS = ∠ABC (alternate angles).
4. With B as the center and radius 6.5 cm, cut ST at D.
5. Join DB and DC: △DBC has the same area as △ABC.
Why it works
△ABC and △DBC stand on the same base BC, and A and D lie on one line ST ∥ BC, so they have the same height. Triangles on the same base and between the same parallels are equal in area.