Question

In the figure AX & CY are respectively the bisectors of the opposite angles A & C of a parallelogram ABCD. Show that AX || CY

Answer 1

Answer:

∠A = ∠C (Opposite angles of parallelogram ABCD)

Therefore, 1/2 ∠A = 1/2 ∠C

i.e., ∠YAX = ∠YCX (1)

Also, ∠AYC + ∠YCX = 180º (Because YA || CX) (2)

Therefore, ∠AYC + ∠YAX = 180º [From (1) and (2)]

So, AX || CY (As interior angles on the same side of the transversal are supplementary)

Answer 2

Answer:

A = ∠C (Opposite angles of parallelogram ABCD) Therefore, 1/2 ∠A = 1/2 ∠C i.e., ∠YAX = ∠YCX (1) Also, ∠AYC + ∠YCX = 180º (Because YA || CX) (2) Therefore, ∠AYC + ∠YAX = 180º [From (1) and (2)] So, AX || CY (As interior angles on the same side of the transversal are supplementary)Read more on Sarthaks.com - https://www.sarthaks.com/871894/fig-and-cy-are-respectively-the-bisectors-of-the-opposite-angles-and-of-parallelogram-abcd