Question

ABCD is a parallelogram. P is the midpoint of
side CD, segment BP meets diagonal AC at X. Prove that
3AX=2AC.​

Answer 1

Answer:3AX = 2AC

Hence proved

Step-by-step explanation:

In the given parallelogram, ABCD

P is midpoint of side CD as shown in figure.

Join BP which intersect diagonal AC at x.

Please find attachment for figure.

In ΔABX and ΔCPX

∠ABX = ∠CPX   ( alternate angle of parallel line, CD||AB)

∠BAX = ∠PCX    ( alternate angle of parallel line, CD||AB)

Therefore, ΔABX ≈ ΔCPX  (By AA similarity property)

If two triangles are similar then their corresponding sides are in proportion.

Therefore,

But  AB = 2PC    (AB=CD opposite side of parallelogram and P is mid point of CD)

CX = AC - AX

Put the value in equation

hence proved

Hope it helps!!!