The third side of an isosceles triangle can be shorter or longer than the other two sides, unlike an equilateral triangle which has all sides equal. Based on sides- Any triangle which has two or more sides equal can be considered as an isosceles triangle. This is known as the defining property of an isosceles triangle.ġ. The two words join together and make the definition which means having two sides and equal lengths. It was named after the Greek word Isosceles which is made up of two words Isos meaning equal and scales meaning legs. The name of the isosceles triangle was found in the mid-18th century. ∠A=∠C (angle corresponding to congruent sides are equal) So, AB = AC (By Congruence) or ∆ABC is isosceles. We have to prove that AC = BC and ∆ABC are isosceles.Ĭonstruct a bisector CD that meets the side AB at right angles. Theorem 2: (Converse) If two angles of a triangle are congruent, then the sides corresponding to those angles are congruent. We need to prove that the angles corresponding to the sides AC and BC are equal, that is, ∠CAB = ∠CBA.įirst, we draw a bisector of angle ∠ACB and name it as a CD.
Proof: Assume an isosceles triangle ABC where AC = BC. Theorem 1: If two sides of a triangle are congruent, then the corresponding angles are congruent
(Converse) If two angles of a triangle are congruent, then the sides corresponding to those angles are congruent. If two sides of a triangle are congruent, then the corresponding angles are congruent.Ģ. An isosceles triangle that has 90 degrees is called a right isosceles triangle.įrom the properties of the Isosceles triangle, the Isosceles triangle theorem is derived.ġ. An isosceles triangle has two equal sides.ģ. The point at which these legs join is called the vertex of the isosceles triangle, and the angle opposite to the hypotenuse is called the vertex angle and the other two angles are called base angles.ġ. These congruent sides are called the legs of the triangle. Here, we will learn about Isosceles and the Equilateral triangle and their theorem, and based on which we will solve some examples.Īn isosceles triangle is a triangle that has at least two congruent sides. Three types of triangles are differentiated based on the length of their vertex. The total sum of the three angles of the triangle is 180 degrees. Students will calculate angles and side lengths of each triangle, match definitions containing angle degrees, and more.A triangle is a polygon with 3 vertices and 3 sides which makes 3 angles.
These worksheets explain how to identify these types of triangles. The radius of an equilateral is half the radius of a circumcircle. You may construct an equilateral triangle of a provided side length using a straightedge and a compass. It is a specific case of a regular polygon, but here, with three sides. The Equilateral has a property with all three interior angles. The examples of the isosceles are the golden triangle, isosceles right triangles, and the faces of bipyramids as well as certain Catalan solids.Įquilateral - This is a triangle that has all three sides equal or of the same length. You can find the other two isosceles triangles if you have one interior angle. These isosceles shapes are used in regular polygon areas plus, the triangles are called 45-45-90. The congruent sides are called legs from the vertex angle, and the other two are base angles. Isosceles - Suppose two sides of a triangle are congruent, the angles that are opposite are congruent. What Are Equilateral and Isosceles Triangles? When it comes to angles of triangles: acute (all angles are acute), right (one right angle), obtuse (one obtuse angle), and equiangulars (you guessed it have all equal angles). If all sides are equal it is called equilateral. The Isosceles Triangle Theorem tells us that if you have an isosceles triangle the angles opposite the congruent sides are also congruent. If two sides of a triangle are congruent that are considered the same in all respects. If the length of two sides of the triangle are equal it is called isosceles. If all the lengths of their sides are different it is scalene. Triangles are often classified by either their number of sides or the measures of their angles.