The length of the base, called the hypotenuse of the triangle, is times the length of its leg. When the base angles of an isosceles triangle are 45°, the triangle is a special triangle called a 45°-45°-90° triangle. Base BC reflects onto itself when reflecting across the altitude.

This triangle has some remarkable properties that we shall prove: The altitudes and sides of ABC are. Leg AB reflects across altitude AD to leg AC. The orthic triangle of ABC is defined to be ABC. The altitude of an isosceles triangle is also a line of symmetry. So, ∠B≅∠C, since corresponding parts of congruent triangles are also congruent. By the Geometric Mean (Leg) Theorem the altitude drawn to the hypotenuse of a right triangle separates. apothem: the perpendicular length from the center of a regular polygon to. Based on this, △ADB≅△ADC by the Side-Side-Side theorem for congruent triangles since BD ≅CD, AB ≅ AC, and AD ≅AD. altitude of a triangle: a line segment drawn or dropped perpendicular from. Using the Pythagorean Theorem where l is the length of the legs. ABC can be divided into two congruent triangles by drawing line segment AD, which is also the height of triangle ABC. Refer to triangle ABC below.ĪB ≅AC so triangle ABC is isosceles. The base angles of an isosceles triangle are the same in measure. Using the Pythagorean Theorem, we can find that the base, legs, and height of an isosceles triangle have the following relationships: In geometry, the altitude is a line that passes through two very specific points on a triangle: a vertex, or corner of a triangle, and its opposite side at a right, or 90-degree, angle.

The height of an isosceles triangle is the perpendicular line segment drawn from base of the triangle to the opposing vertex. The angle opposite the base is called the vertex angle, and the angles opposite the legs are called base angles. Parts of an isosceles triangleįor an isosceles triangle with only two congruent sides, the congruent sides are called legs. DE≅DF≅EF, so △DEF is both an isosceles and an equilateral triangle.

Length altitude geometry definition