7/29/2023 0 Comments Isosceles triangleThe apothem of a regular polygon is also the height of an isosceles triangle formed by the center and a side of the polygon, as shown in the figure below.įor the regular pentagon ABCDE above, the height of isosceles triangle BCG is an apothem of the polygon. 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. An isosceles triangle definition states it as a polygon that consists of two equal sides, two equal angles, three edges, three vertices and the sum of internal angles of a triangle equal to 1800. Leg AB reflects across altitude AD to leg AC. The altitude of an isosceles triangle is also a line of symmetry. So, ∠B≅∠C, since corresponding parts of congruent triangles are also congruent. For any three similar shapes of area on the sides of a right triangle, (2) which is equivalent to the Pythagorean theorem. Based on this, △ADB≅△ADC by the Side-Side-Side theorem for congruent triangles since BD ≅CD, AB ≅ AC, and AD ≅AD. Special cases of the right triangle include the isosceles right triangle (middle figure) and 30-60-90 triangle (right figure). 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: Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. The height of an isosceles triangle is the perpendicular line segment drawn from base of the triangle to the opposing vertex. In geometry, an isosceles triangle ( / assliz /) is a triangle that has two sides of equal length. 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.
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