In an equilateral triangle, all angles will be 60°. The 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. An isosceles triangle will have two angles the same size. The length of the base, called the hypotenuse of the triangle, is times the length of its leg. The congruent sides of the isosceles triangle are called the legs. When the base angles of an isosceles triangle are 45°, the triangle is a special triangle called a 45°-45°-90° triangle. An isosceles triangle is a triangle that has at least two congruent sides. Base BC reflects onto itself when reflecting across the altitude. The angles opposite the equal sides are also equal. 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. Based on this, △ADB≅△ADC by the Side-Side-Side theorem for congruent triangles since BD ≅CD, AB ≅ AC, and AD ≅AD. Using the Pythagorean Theorem where l is the length of the legs. Isosceles triangles are those triangles that have two sides of equal measure. In the triangle ABC, BC is the base of the isosceles triangle. Base: The ‘base’ of an isosceles triangle is the third and unequal side. In the triangle ABC (given above), AB and AC are the two legs of the isosceles triangle. ABC can be divided into two congruent triangles by drawing line segment AD, which is also the height of triangle ABC. Legs: The two equal sides of an isosceles triangle are known as ‘legs’. 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: 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.
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