No, you cannot, if you are trying to do them on the same 2-D plane.
If the plane is 3-D, and you are talking about more than one plane,
then yes it is possible.
(A "3-D" plane ? ? ? Well, OK.)
If you get a chance, take a quick look at the corner of your room,
where two walls and the floor all come together.
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Perpendicular lines are lines that intersect at a 90-degree angle. In two dimensions, perpendicular lines form right angles, which are commonly found in the shape of a square, rectangle, or any other quadrilateral with perpendicular sides. In three dimensions, perpendicular lines can form the edges of a cube or rectangular prism.
To find a point equidistant from three other points, construct perpendicular bisectors for two of the segments formed from three points. Note: this will be the center of the circle that has all three points on it's circumference. Three points, not in a straight line, form three pairs of points with each pair defining a different line. Take any pair of points and draw the perpendicular bisector of the line joining them. Repeat for one of the other pairs. These two perpendicular bisectors will meet at the point which is equidistant from all three points - the circumcenter of the triangle formed by the three points.
A three-sided shape with one pair of perpendicular lines is called a right triangle. In a right triangle, one angle is a right angle (90 degrees), which means that one pair of sides are perpendicular to each other. The other two angles are acute, measuring less than 90 degrees. The Pythagorean theorem can be used to find the lengths of the sides of a right triangle.
A square, a rhombus and a kite are three examples of quadrilaterals that have perpendicular diagonals that intersect each other at right angles.
A triangle can have one angle made up of perpendicular lines. That would be called a right triangle. A triangle cannot have more than one angle made up of perpendicular lines however. To see why, remember that an angle created by two perpendicular lines is 90 degrees and a triangle is made up of three angles that sum to 180 degrees. If two angles were 90 degrees the third angle would have to be 0 degrees, in which case the shape is no longer a triangle.