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
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