PQRS IS A RECTANGLE AB=25CM, BC=15CM .IN WHAT RATIO DOES BISECTOR OF ANGLE C DIVIDES AB?
To find the ratio in which the bisector of angle C divides AB, we need to consider the properties of the angle bisector.
Given:
PQRS is a rectangle with sides PQ and QR parallel to AB.
AB = 25 cm and BC = 15 cm.
To find the ratio, we need to find the lengths of the two segments that the bisector divides AB into. Let's label the point where the bisector intersects AB as X.
To find the length of AX, we can use the property that the angle bisector divides the opposite side into segments proportional to the adjacent sides. In this case, the opposite side is QR, and the adjacent sides are PQ and QS.
Using the angle bisector theorem, we can set up the following proportion:
AX / BX = PQ / QS
Since PQ and QS are sides of a rectangle, they are equal. Therefore, the equation becomes:
AX / BX = PQ / PQ
Simplifying the equation, we get:
AX / BX = 1
This means that AX is equal in length to BX. Therefore, the bisector divides AB into two equal-length segments.
So, the ratio in which the bisector of angle C divides AB is 1:1, or in other words, it divides AB into two equal parts.