Question

Diagonals of quadrilateral ABCD intersects at point Q if 2QA=QC 2QB=QD then prove that DC=2AB​

Answer 1

Given: Diagonals of quadrilateral ABCD intersects at point Q.

To find: Prove that DC=2AB​

Solution:

• Now we have given that diagonals of quadrilateral ABCD intersects at point Q.

• We have also given: 2QA = QC and 2QB = QD

• Dividing both, we get:

                 2QA/2QB = QC/QD

                 QA/QB = QC/QD

                 QA/QC = QB/QD

• Now ∠AQB = ∠CQD ..................( Vertically opposite angles)

• Now comparing triangles QAB and QCD, we get:

                 QA / QC  = QB / QD          

                 ∠AQB = ∠CQD

• So from above two, we get:

                 triangle QAB ≈ triangle QCD

                 QA/QC  = AB/CD

                 1/2 = AB/CD

                 CD = 2 x AB

• Hence proved

Answer:

              So we proved that CD = 2 x AB

Answer 2

Step-by-step explanation:

answer sheet is attached