20 - The values "a = 16" and "b = 14" ensure that opposite sides of the given quadrilateral are equal, confirming its status as a parallelogram according to the specified property. 21 - For the second quadrilateral, the corresponding values are a = 29/4 and b = 13/2.
21 - To find the values of a and b that make the given quadrilateral a parallelogram, we use the property that opposite sides of a parallelogram are equal.
For the first pair of opposite sides, we set up the equation "2a + 6 = 3a - 10". By simplifying, we find "a = 16".
For the second pair of opposite sides, we set up the equation "5a + 1 = 6b - 3". Substituting "a = 16", we can solve for "b". After solving, we get "b = 14".
Therefore, the values "a = 16" and "b = 14" make the quadrilateral a parallelogram, satisfying the property that opposite sides are equal.
22 - In order to make the quadrilateral a parallelogram, the opposite sides must be parallel and equal in length. Therefore, we need to solve the following equations:
5b - 7 = 3b + 6
2a = 3b - 5
Solving for b in the first equation, we get:
5b - 3b = 6 + 7
2b = 13
b = 13/2
Substituting b = 13/2 in the second equation, we get:
2a = 3(13/2) - 5
2a = 39/2 - 10/2
2a = 29/2
a = 29/4
Therefore, the values of a and b that would make the quadrilateral a parallelogram are:
a = 29/4
b = 13/2