In geometry, the altitude of a triangle is a perpendicular segment drawn from a vertex to the line containing the opposite side (called the base). The altitude represents the triangle’s height (h) and is used in the area formula: Area = ½ × base × height. Every triangle has three altitudes, one from each vertex. In a right triangle, two of the three altitudes are the legs themselves. The altitude-area relationship appears on the SAT Math section in triangle geometry problems.
An altitude is a segment from a vertex of a triangle, drawn perpendicular to the opposite side (or the line containing it). In a right triangle, the altitude to the hypotenuse creates three similar triangles, a relationship the SAT loves to test.
An altitude is a perpendicular segment from a vertex to the opposite side. Every triangle has three altitudes, and they meet at a single point called the orthocenter. The altitude is also the “height” used in the area formula: Area = ½ · base · altitude.
The altitude to the hypotenuse is drawn from the right angle of a right triangle, perpendicular to the hypotenuse. It divides the original triangle into two smaller right triangles and all three triangles are similar to each other.
Why this matters for the SAT: those similarity relationships let you set up proportions among the altitude, the segments of the hypotenuse, and the legs often solving for a missing length without any trigonometry.
Drawing the altitude to the hypotenuse splits the right triangle into three triangles that are all similar, so their sides are proportional.
The full right triangle, with the right angle at the top vertex.
Formed on the left of the altitude similar to the original.
Formed on the right of the altitude also similar to the original.
When the altitude splits the hypotenuse into two segments p and q (so the full hypotenuse c = p + q):
h = altitude to the hypotenuse · p, q = the two hypotenuse segments it creates. The altitude is the geometric mean of the two segments.
c = full hypotenuse. Each leg is the geometric mean of the hypotenuse and the segment of the hypotenuse next to it.
Worked example. The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of 4 and 9 . Find the altitude.
The altitude is the geometric mean of the two hypotenuse segments a fast SAT shortcut that avoids trigonometry.
When a right triangle has a segment drawn from the right angle to the hypotenuse, think "three similar triangles" immediately.
Match corresponding sides across the similar triangles and cross-multiply no trig needed.
Altitude = √(p·q); each leg = √(c · adjacent segment). Memorizing these saves real time.
An altitude is perpendicular to the opposite side; a median goes to its midpoint. They're usually different segments.
For the leg rule, pair each leg with the hypotenuse segment adjacent to it not the far one.
The altitude must meet the base at 90°. If it isn't perpendicular, it isn't an altitude.
A perpendicular segment from a vertex of a triangle to the opposite side (or the line containing it). It's the "height" used in the area formula, Area = ½ · base · altitude.
Each smaller triangle shares an angle with the original and has a right angle, so by Angle-Angle similarity all three triangles are similar which makes their corresponding sides proportional.
If the altitude splits the hypotenuse into segments p and q, then altitude = √(p · q) the geometric mean of the two segments.
An altitude is perpendicular to the opposite side; a median connects a vertex to the midpoint of the opposite side. They coincide only in special cases (like the equal sides of an isosceles triangle).
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