Question

In Quardilateral ABCD , side BC || AD . Diagonal AC and diagonal BD intersect in point Q. If AQ=1/3AC , then show that DQ =1/2BQ​

Answer 1

Given: in quadrilateral ABCD,

AD ║ BC  and  AQ=1/3 AC

To prove:  DQ=1/2 BQ

Proof:

Since, AQ=1/3 AC

⇒ AQ/AC = 1/3

Let, AQ = x and AC = 3x

Where x is any number,

⇒ CQ = AC - AQ = 3x - x = 2x

Now, In quadrilateral ABCD,

AD ║ BC

By the Alternative interior angle theorem,

,

By AA similarity postulate,

Now, By the property of similar triangles,

Hence, Proved.