The length of the base, called the hypotenuse of the triangle, is times the length of its leg. An isosceles triangle has two equal sides and two equal angles. This property is equivalent to two angles of the triangle being equal. 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 any of its two sides equal in length. Base BC reflects onto itself when reflecting across the altitude. Isosceles triangles are very helpful in determining unknown angles.
If all three side lengths are equal, the triangle is also equilateral. Leg AB reflects across altitude AD to leg AC. An isosceles triangle is a triangle that has (at least) two equal side lengths. 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. When the third angle is 90 degree, it is called a right isosceles triangle. It has two equal angles, that is, the base angles. Some pointers about isosceles triangles are: It has two equal sides. ABC can be divided into two congruent triangles by drawing line segment AD, which is also the height of triangle ABC. An isosceles triangle is a triangle which has two equal sides, no matter in what direction the apex (or peak) of the triangle points. 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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