Opposite angles are equal. Opposite sides are also parallel. Therefore, if the horizontal line and vertical line are perpendicular to each other, this must remain so for every other angle, meaning that, in this case, they are all the same.
Opposite angles in a parallelogram are equal, so with one angle marked as 90°, we know the angle opposite is also 90°. The other two angles are equal, and since the sum of the interior angles of a convex quadrilateral is 360°, these two equal angles must have a sum of 180°, meaning they are both also 90°, which means all 4 interior angles are 90°, making the quadrilateral a rectangle.
If you have a parallelogram, and one side has a right angle (90Ë), then the oposite side has to have a right angle(function of parallelograms, look in your textbook for further theorems), meaning that you now have two sides with a total of 180 degrees.
(Sorry for the periods :P)
____________________
| 90Ë.............................|
|...................................|
|_________________90Ë|
A definition of a parallelogram states that all sides have to add up to 360Ë, so by subtracting, you can tell that the last two angles add up to 180Ë. Dividing the 180Ë in two will give you your last two angles (similar to the function that we used above, if you have any questions about all the functions of a parallelogram, you can just google them).
Comments
Opposite angles are equal. Opposite sides are also parallel. Therefore, if the horizontal line and vertical line are perpendicular to each other, this must remain so for every other angle, meaning that, in this case, they are all the same.
Opposite angles in a parallelogram are equal, so with one angle marked as 90°, we know the angle opposite is also 90°. The other two angles are equal, and since the sum of the interior angles of a convex quadrilateral is 360°, these two equal angles must have a sum of 180°, meaning they are both also 90°, which means all 4 interior angles are 90°, making the quadrilateral a rectangle.
If you have a parallelogram, and one side has a right angle (90Ë), then the oposite side has to have a right angle(function of parallelograms, look in your textbook for further theorems), meaning that you now have two sides with a total of 180 degrees.
(Sorry for the periods :P)
____________________
| 90Ë.............................|
|...................................|
|_________________90Ë|
A definition of a parallelogram states that all sides have to add up to 360Ë, so by subtracting, you can tell that the last two angles add up to 180Ë. Dividing the 180Ë in two will give you your last two angles (similar to the function that we used above, if you have any questions about all the functions of a parallelogram, you can just google them).
____________________
| 90Ë........................90Ë|
|..................................|
|90Ë______________90Ë|