2. Diagonals of a trapezium ABCD with AB : DC intersect each other at the point 0.
If AB = 2 CD, find the ratio of the
areas of triangles AOB and COD.
Answers
Answer:
Given,
Given,ABCD is a trapezium with AB∣∣CD
Given,ABCD is a trapezium with AB∣∣CD And
Given,ABCD is a trapezium with AB∣∣CD And AB=2CD
Given,ABCD is a trapezium with AB∣∣CD And AB=2CD In the triangles AOB and COD,
Given,ABCD is a trapezium with AB∣∣CD And AB=2CD In the triangles AOB and COD,∠DOC=∠BOA [vertically opposite angles are equal]
Given,ABCD is a trapezium with AB∣∣CD And AB=2CD In the triangles AOB and COD,∠DOC=∠BOA [vertically opposite angles are equal]∠CDO=∠ABO [alternate interior angles ]
Given,ABCD is a trapezium with AB∣∣CD And AB=2CD In the triangles AOB and COD,∠DOC=∠BOA [vertically opposite angles are equal]∠CDO=∠ABO [alternate interior angles ]∠DCO=∠BAO
Given,ABCD is a trapezium with AB∣∣CD And AB=2CD In the triangles AOB and COD,∠DOC=∠BOA [vertically opposite angles are equal]∠CDO=∠ABO [alternate interior angles ]∠DCO=∠BAO Thus,
Given,ABCD is a trapezium with AB∣∣CD And AB=2CD In the triangles AOB and COD,∠DOC=∠BOA [vertically opposite angles are equal]∠CDO=∠ABO [alternate interior angles ]∠DCO=∠BAO Thus,△AOB≈△COD
Given,ABCD is a trapezium with AB∣∣CD And AB=2CD In the triangles AOB and COD,∠DOC=∠BOA [vertically opposite angles are equal]∠CDO=∠ABO [alternate interior angles ]∠DCO=∠BAO Thus,△AOB≈△CODBy the similarity rule, the ratio of the areas of the similar triangles is the ratio of the square of corresponding sides.
Given,ABCD is a trapezium with AB∣∣CD And AB=2CD In the triangles AOB and COD,∠DOC=∠BOA [vertically opposite angles are equal]∠CDO=∠ABO [alternate interior angles ]∠DCO=∠BAO Thus,△AOB≈△CODBy the similarity rule, the ratio of the areas of the similar triangles is the ratio of the square of corresponding sides.t
