A triangle from its measures
Construct △ABC with BC = 4.5 cm, AB = 5 cm and AC = 6.5 cm.
Construct △ABC with BC = 6.6 cm, AB = 7 cm and AC = 6 cm.
Construct △ABC with BC = 5.2 cm, AB = 5.5 cm and AC = 5.5 cm.
Construct △ABC with BC = 5.6 cm, ∠ABC = 60° and AB = 4.5 cm.
Construct △ABC with BC = 5 cm, ∠ABC = 75° and AB = 4.8 cm.
Construct △ABC with BC = 5.8 cm, ∠ABC = 45° and AB = 5 cm.
Construct △ABC with BC = 5.2 cm, ∠ABC = 75° and ∠ACB = 60°.
Construct △ABC with BC = 6 cm, ∠ABC = 60° and ∠ACB = 45°.
Construct △ABC with BC = 6.8 cm, ∠ABC = 75° and ∠ACB = 30°.
Construct △ABC with BC = 5 cm, ∠ABC = 45° and ∠BAC = 75°.
Construct △ABC with BC = 6 cm, ∠ABC = 60° and ∠BAC = 90°.
Construct △ABC with BC = 5.5 cm, ∠ABC = 45° and ∠BAC = 60°.
1. Draw BC = 4.5 cm.
2. With B as the center and radius 5 cm, draw an arc above BC.
3. With C as the center and radius 6.5 cm, draw an arc that cuts the first one at A.
4. Join AB and AC: △ABC is the triangle.
1. Draw BC = 6.6 cm.
2. With B as the center and radius 7 cm, draw an arc above BC.
3. With C as the center and radius 6 cm, draw an arc that cuts the first one at A.
4. Join AB and AC: △ABC is the triangle.
1. Draw BC = 5.2 cm.
2. With B as the center and radius 5.5 cm, draw an arc above BC.
3. With C as the center and radius 5.5 cm, draw an arc that cuts the first one at A.
4. Join AB and AC: △ABC is the triangle.
1. Draw BC = 5.6 cm.
2. At B, construct ∠CBX = 60°.
3. With B as the center and radius 4.5 cm, cut BX at A.
4. Join AC: △ABC is the triangle.
1. Draw BC = 5 cm.
2. At B, construct ∠CBX = 75°.
3. With B as the center and radius 4.8 cm, cut BX at A.
4. Join AC: △ABC is the triangle.
1. Draw BC = 5.8 cm.
2. At B, construct ∠CBX = 45°.
3. With B as the center and radius 5 cm, cut BX at A.
4. Join AC: △ABC is the triangle.
1. Draw BC = 5.2 cm.
2. At B, construct ∠CBX = 75°.
3. At C, construct ∠BCY = 60°.
4. BX and CY meet at A: △ABC is the triangle.
1. Draw BC = 6 cm.
2. At B, construct ∠CBX = 60°.
3. At C, construct ∠BCY = 45°.
4. BX and CY meet at A: △ABC is the triangle.
1. Draw BC = 6.8 cm.
2. At B, construct ∠CBX = 75°.
3. At C, construct ∠BCY = 30°.
4. BX and CY meet at A: △ABC is the triangle.
1. Draw BC = 5 cm.
2. The angles of a triangle add up to 180°, so ∠ACB = 180° − (45° + 75°) = 60°.
3. At B, construct ∠CBX = 45°.
4. At C, construct ∠BCY = 60°.
5. BX and CY meet at A: △ABC is the triangle, with ∠BAC = 75°.
1. Draw BC = 6 cm.
2. The angles of a triangle add up to 180°, so ∠ACB = 180° − (60° + 90°) = 30°.
3. At B, construct ∠CBX = 60°.
4. At C, construct ∠BCY = 30°.
5. BX and CY meet at A: △ABC is the triangle, with ∠BAC = 90°.
1. Draw BC = 5.5 cm.
2. The angles of a triangle add up to 180°, so ∠ACB = 180° − (45° + 60°) = 75°.
3. At B, construct ∠CBX = 45°.
4. At C, construct ∠BCY = 75°.
5. BX and CY meet at A: △ABC is the triangle, with ∠BAC = 60°.
Why it works
Each set of measures fixes the triangle: the base is drawn first, and the third corner is where two things it must satisfy meet. For SSS it is two arcs (the right distances from B and C); for SAS an arm and an arc; for ASA two arms. Given the angle opposite the base instead, the angles add up to 180°, so the other angle on the base is known and it is ASA again. Any two triangles drawn from the same measures are congruent.