Parallelogram PQRS with 2 diagonals PR and QS intersecting at point T. Segment PT is labeled (a plus 4) units. Segment RT is labeled 2a units. Segment QT is labeled b units. Segment ST is labeled (2b minus 3) units.
To find the values of a and b, we can use the fact that the diagonals of a parallelogram bisect each other.
Since PT and RT are diagonals of the parallelogram, they bisect each other at point T. This means that PT is equal to RT, so we can write the equation:
(a + 4) = 2a
Simplifying this equation gives:
4 = a
Similarly, since QT and ST are diagonals of the parallelogram, they bisect each other at point T. This means that QT is equal to ST, so we can write the equation:
b = 2b - 3
Simplifying this equation gives:
3 = b
Therefore, the value of a is 4 and the value of b is 3.