An altitude is the perpendicular segment from a vertex of a triangle to the line containing the opposite side. These activities let you watch the three altitudes and their meeting point move as a triangle changes shape, name the special segments drawn in a triangle, and solve for missing values.
An altitude of a triangle is the perpendicular segment from a vertex to the line containing the opposite side. Unlike a median, an altitude is defined by a right angle, not by a midpoint — and in an obtuse triangle the altitude from an acute vertex lands outside the triangle, on the extension of the opposite side. The three altitudes meet at the orthocenter. In an isosceles triangle, the altitude from the vertex angle does extra duty: it is also the median, the angle bisector, and the perpendicular bisector of the base.
What to do: Drag any vertex of the triangle. Use the From A, From B, From C, and All Three buttons to choose which altitudes are drawn — each altitude always keeps its own color. A right-angle mark shows where each altitude lands, on a side or on that side's extension.
Choose which altitudes are drawn. Each altitude keeps its own color in every view: blue from A, red from B, green from C.
These buttons set the triangle to one of the three types. In an obtuse triangle, watch an altitude land outside the triangle, on a side's extension.
Drag any orange handle to change the triangle yourself. The altitudes redraw as you drag, and a side's line is drawn out in a lighter stroke whenever an altitude lands on its extension.
What to do: Drag any vertex of the triangle, or use the three buttons to jump to an acute, right, or obtuse triangle. All three altitudes are drawn in their own colors. When the orthocenter falls outside the triangle, the altitudes are continued with dashed lines so they can intersect there.
These buttons set the triangle to one of the three types. Watch the orthocenter: inside, at a vertex, or outside.
Drag any orange handle to change the triangle yourself. The altitudes, their dashed continuations, and the orthocenter redraw as you drag.
What to do: Answer each problem from what the diagram shows. Marks mean what they always mean: a small square is a right angle, matching tick marks are equal lengths, and matching angle marks are equal angles. A first miss gives a hint and another try; the Next item button cycles through all ten problems in order.
What to do: Work each problem one step at a time. Step 1 chooses the statement or equation that governs the problem. A first miss gives a hint and another try. The gold wedge marks the part the current step asks about, and a part solved in an earlier step is labeled with its found value.
What to do: Answer all six questions. A first miss gives a hint and another try; after a second miss the answer is shown and explained. Your score counts first-try answers only.
Altitudes — Mr. J Geometry. All activities on this page run entirely in your browser.