# In Fig.8.4, AX and CY are respectively the bisectors of the opposite angles A and C of a parallelogram ABCD. Show that AX || CY.

**Solution:**

Given, ABCD is a __parallelogram__

AX and CY are the bisectors of the angles A and C.

We have to show that AX || CY

∠DAB = 2x

∠DCB = 2y

We know that opposite angles of a parallelogram are equal.

So, ∠A = ∠C

2x = 2y

x = y

As DC || AB, XC || AY

∠XCY = ∠CYB [Alternate angles]

∠CYB = x

∠XAY = x

As ∠XAY and ∠CYB are corresponding angles

AX || CY

Therefore, AX is parallel to CY.

**✦ Try This: **In the given Figure, ABCD is a parallelogram, AE⊥DC and CF⊥AD. If AB = 16 cm,AE = 8 cm and CF = 10 cm, find AD.

**☛ Also Check:** NCERT Solutions for Class 9 Maths Chapter 8

**NCERT Exemplar Class 9 Maths Exercise 8.3 Sample Problem 3**

## In Fig.8.4, AX and CY are respectively the bisectors of the opposite angles A and C of a parallelogram ABCD. Show that AX || CY

**Summary: **

In Fig.8.4, AX and CY are respectively the bisectors of the opposite angles A and C of a parallelogram ABCD. It is shown that AX || CY

**☛ Related Questions:**

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