ΔSTR is isosceles and 𝑇𝑈 bisects ∠STR Therefore, ∠TUS is a right angle and 𝑆𝑈 ≅ 𝑈𝑅ġ0 Theorem 51-4 If a line is the perpendicular bisector of the base of an isosceles triangle, then it bisects the vertex angle. If a triangle is equiangular, then it is equilateral.ĩ Theorem 51-3 If a line bisects the vertex angle of an isosceles triangle, then it is the perpendicular bisector of the base. Yes What can you conclude about all three sides of an equiangular triangle? Why? They are all congruent In ΔABC, ∠B ≅ ∠C ≅ ∠A Therefore, 𝐴𝐶 ≅ 𝐵𝐴 ≅ 𝐶𝐵Ĩ Corollaries of Equilateral & Equiangular TrianglesĬorollary Corollary If a triangle is equilateral, then it is equiangular. If two angles of a triangle are congruent, then the sides opposite those angles are also congruent. They are all congruent ∠G & ∠H are base angles so ∠G ≅ ∠H ∠F & ∠H are also base angles so ∠F ≅ ∠H Therefore, using the transitive property all three angles are congruentĦ Theorem 51-2: Converse of the Isosceles Triangle Theorem Yes, because equilateral triangles are also isosceles What can you conclude about all three angles of an equilateral triangle? Explain. ∆𝑅𝑆𝑇 is isosceles Therefore, ∠𝑆≅∠𝑅ĥ Can you apply Theorem 51-1 to equilateral triangles? Why? If a triangle is isosceles, then its base angles are congruent. In an isosceles triangle, the two sides are equal, and the two angles at the base are also equal.

One of these theorems is that the base angles are equal.

In addition, all isosceles triangles also have congruent base angles. Also, isosceles triangles have a property (theorem) derived from their definition. Of course, the main property of isosceles triangles is their two congruent sides. An equilateral triangle has all sides congruent and is equiangular meaning. Properties Two equal (congruent) sides in ABC, AB and AC are two congruent sides One line of symmetry The two angles opposite to the equal sides are equal. Lesson 51 Properties of Isosceles & Equilateral TrianglesĢ Review Vocabulary An equilateral triangle has all congruent sides ΔFGH An equiangular triangle has all congruent angles ΔABC An isosceles triangle has at least 2 congruent sides ΔJIKģ New Vocabulary A leg of an isosceles triangle is one of the two congruent sides 𝑆𝑇 & 𝑅𝑇 The vertex angle of an isosceles triangle is the angle formed by the legs ∠T The base of an isosceles triangle is the side opposite the vertex angle 𝑅𝑆 A base angle of an isosceles triangle is one of the two angles that have the base as a side (not the vertex angle) ∠S & ∠RĤ Theorem 51-1: Isosceles Triangle Theorem If you are given an isosceles triangle in a math problem, the two sides have the same length. An isosceles triangle has exactly 2 congruent sides and exactly 2 congruent angles. – The term scalene triangle is derived from Late Latin ‘scalēnus’ and from the Ancient Greek word ‘σκᾰληνός’ which means unequal or uneven.Presentation on theme: 'Properties of Isosceles & Equilateral Triangles'- Presentation transcript:ġ Properties of Isosceles & Equilateral Triangles In this triangle, angle E will be the greatest angle as it is opposite to the greatest side GO and angle O will be the smallest angle as it is opposite to the smallest side GE.Ī scalene triangle can be acute-angled or obtuse-angled or right-angled. Often abstract or complicated shapes are broken into. Many triangles found in the real world can be considered isosceles, including a section of a slice of pizza. Isosceles Triangle Properties, Characteristics & Uses.

The given triangle cannot be divided into two identical halves. These words make a difference when considering if a triangle is also an equilateral triangle as well as an isosceles triangle. The angle opposite to the longest side would be the greatest angle and vice versa.Īll sides of the given scalene triangle are unequal. Properties of the scalene triangle: All angles of a scalene triangle are unequal.Ī scalene triangle has no line of symmetry. (iii) Scalene triangle: if none of the three sides of a triangle are equal to each other, it is called a scalene triangle. (ii) Isosceles triangle: If two sides of a triangle are equal, then it is called an isosceles triangle. (i) Equilateral triangle: If all sides of a triangle are equal, then it is called an equilateral triangle. We can classify triangles according to the length of their sides. A triangle is a polygon made up of 3 sides and 3 angles.

Properties of isosceles triangles