How do you know if a Triangle is Isosceles?Ī triangle can be scalene, isosceles, or equilateral when classified on the basis of the length of its sides. The converse of isosceles triangle theorem is also true which states that in a triangle if two angles are equal then the sides opposite to those angles are also equal. The isosceles triangle theorem states that when two sides are equal, the base angles are also equal. Following this fact, if two sides of a triangle are equal, then the angles opposite to those sides are also equal. The perpendicular bisector drawn from any angle bisects that angle and the side opposite to it.Ĭheck out a few more interesting articles related to the isosceles triangle in math.įAQs on Isosceles Triangle What is an Isosceles Triangle?Ī triangle in which at least two sides are equal is called an isosceles triangle.
The perpendicular bisector drawn from the apex angle bisects that angle and the unequal side of the triangle. CriteriaĪll three sides are of different measurements.Īt least two angles are equal in measure.Īll three angles are equal and measure 60 degrees each. Look at the table below to understand the differences and similarities in scalene, equilateral, and isosceles triangles. A scalene triangle is the one in which all three sides and all three angles are of different measurements, an equilateral triangle is the one with all three sides and angles equal, and in an isosceles triangle, two sides and two angles are equal in measurement. Each triangle is different from the other on the basis of its unique properties. The three common types of triangles are scalene, equilateral, and isosceles triangles.
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.Scalene Equilateral and Isosceles Triangle 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. 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. 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: 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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