A triangle equal to a quadrilateral
Construct quadrilateral ABCD with AB = 5 cm, BC = 4.4 cm, CD = 3.6 cm, DA = 4 cm and the diagonal AC = 6.4 cm. Then construct △AED of the same area, with E on AB produced.
Construct quadrilateral ABCD with AB = 5 cm, BC = 4 cm, CD = 3.5 cm, DA = 4 cm and the diagonal AC = 6 cm. Then construct △AED of the same area, with E on AB produced.
Construct quadrilateral ABCD with AB = 5.5 cm, BC = 5.5 cm, CD = 4.5 cm, DA = 4.5 cm and ∠DAB = 75°. Then construct △AED of the same area, with E on AB produced.
Construct quadrilateral ABCD with AB = 4.5 cm, BC = 4 cm, CD = 4.5 cm, DA = 3.5 cm and the diagonal AC = 6 cm. Then construct △AED of the same area, with E on AB produced.
1. Draw AB = 5 cm.
2. With A as the center and radius 6.4 cm, and B as the center and radius 4.4 cm, draw arcs that cut at C. Join AC and BC.
3. With A as the center and radius 4 cm, and C as the center and radius 3.6 cm, draw arcs that cut at D. Join AD and CD: ABCD is the given quadrilateral.
4. Join the diagonal DB.
5. Through C, draw a line parallel to DB by copying ∠DBC at C (alternate angles).
6. Produce AB to meet that line at E.
7. Join DE: △AED has the same area as ABCD.
1. Draw AB = 5 cm.
2. With A as the center and radius 6 cm, and B as the center and radius 4 cm, draw arcs that cut at C. Join AC and BC.
3. With A as the center and radius 4 cm, and C as the center and radius 3.5 cm, draw arcs that cut at D. Join AD and CD: ABCD is the given quadrilateral.
4. Join the diagonal DB.
5. Through C, draw a line parallel to DB by copying ∠DBC at C (alternate angles).
6. Produce AB to meet that line at E.
7. Join DE: △AED has the same area as ABCD.
1. Draw AB = 5.5 cm.
2. At A, construct ∠DAB = 75° and cut AD = 4.5 cm on its arm.
3. With B as the center and radius 5.5 cm, and D as the center and radius 4.5 cm, draw arcs that cut at C. Join BC and DC: ABCD is the given quadrilateral.
4. Join the diagonal DB.
5. Through C, draw a line parallel to DB by copying ∠DBC at C (alternate angles).
6. Produce AB to meet that line at E.
7. Join DE: △AED has the same area as ABCD.
1. Draw AB = 4.5 cm.
2. With A as the center and radius 6 cm, and B as the center and radius 4 cm, draw arcs that cut at C. Join AC and BC.
3. With A as the center and radius 3.5 cm, and C as the center and radius 4.5 cm, draw arcs that cut at D. Join AD and CD: ABCD is the given quadrilateral.
4. Join the diagonal DB.
5. Through C, draw a line parallel to DB by copying ∠DBC at C (alternate angles).
6. Produce AB to meet that line at E.
7. Join DE: △AED has the same area as ABCD.
Why it works
△DBC and △DBE stand on the same base DB, and C and E lie on one line parallel to DB, so they are equal in area. Add △ABD to both: ABCD = △ABD + △DBC = △ABD + △DBE = △AED.