Base and height

The figure shows triangle F G H. Two lines are drawn in dashes. F J, which meets G H at a right angle, and H K, which meets F G at a right angle. F G is taken as the base of the triangle. Which line is the height of triangle F G H? This is one triangle, drawn 3 times. Same corners, same sides, same size. The corners are A, B and C in all 3. A base is a side you choose to stand the triangle on, and any of the 3 sides can be chosen. In the first triangle, choose A C. The corner A C does not touch is B, and the height runs from B to A C. It meets A C at a right angle, and the small square at X says so. This height is inside the triangle. Now the second one. Choose B C as the base. B C is the base, and the corner B C does not touch is A. The line from A cannot meet B C between B and C, so B C is extended past B. A Y is that line, and the square at Y says it meets the extended base at a right angle. A Y is outside the triangle, and A Y is still the height. All a height has to be is perpendicular to its base. The third takes A B as the base. The corner A B does not touch is C, and A B is extended past B as well. C Z meets that extended base at a right angle, so C Z is the height for A B. One triangle, 3 bases, 3 heights, and each points a different way. So the height follows the base. Choose a different base and the height is a different line. Two dashed lines, and only one is the height we were asked for. F G is the side we were given, so F G is the base. The corner F G does not touch is H, so the height starts at H. F J starts at F and meets G H, so F J is the height when G H is the base. H K starts at H and meets F G at a right angle. So H K is the height of triangle F G H.

Your turn. The figure shows triangle S T U. U T is extended to V, and S V is drawn to meet it at a right angle. T W is drawn from T to meet S U at a right angle. T U is taken as the base of the triangle. Which line is the height of triangle S T U? Try it first. Pause if you like. T U is the side we were given, so T U is the base. The corner T U does not touch is S, so the height starts at S. T W starts at T and meets S U, so T W is the height when S U is the base. The corner at T leans back over T U, so the line from S lands past T. That is why U T is extended to V. S V meets the base extended at a right angle, so S V is the height of triangle S T U. The base is a choice. The height is whatever is perpendicular to the base you chose.