No.
An isotherm is a collection of points that are all at the same temperature. If two (different) isotherms were to touch each other then that would imply that they were at the same temperature but, by definition, if they have points on them at different temperatures then all the points on them must be at different temperatures.
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No. Two isotherms have different temperatures. If they intersected, the intersection point would have two temperatures at once, which is not possible.
their slopes are negative reciprocals of each other. and they make a right angle when they intersect.
This is true. If three straight lines are drawn, they can only intersect at two points. That is, each line will only intersect with another once.
When two lines cross each other they form vertical equal opposite angles
perpendicular lines intersect each other at 90 degrees whereas parallel lines never intersect each other and remain equal distance apart from each other. Obviously the way to test if two lines are parallel is to measure their distance from each other at at least two points (the farther apart the better) to confirm that they remain equal distance apart, but to test if lines are perpendicular, with a compass with the point at the point where the two lines intersect, draw an arc (or three parts of an arc) that intersects one of the lines in two places and the other line in one place. If the distances between the lines at the points where they are intersected by the arc are equal, the lines are perpendicular.
Two planes intersect at a line