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Exploring Isosceles and Equilateral Triangles: Theorems and Properties

Dive into the fundamental theorems and properties of isosceles and equilateral triangles, including base angles, symmetry lines, and congruence relationships. Understand the symmetry, congruence, and angles involved in these special types of triangles.

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Exploring Isosceles and Equilateral Triangles: Theorems and Properties

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  1. Isosceles and EquilateralTriangles Section 5-1

  2. Isosceles Triangle • A triangle with at least two congruent sides. Vertex Angle Leg Leg Base Angles Base

  3. Equilateral Triangle • A triangle with all equal sides.

  4. Theorems • Theorem 5-1 (Isosceles Triangle Theorem) • The base angles of an isosceles triangle are congruent • Theorem 5-2 • The line of symmetry for an isosceles triangle • 1. Bisects the vertex angle • 2. Is the perpendicular bisector of the base.

  5. Theorems (con’t) • Theorem 5-3 • If two angles of a triangle are congruent, then the sides opposite those angles are congruent • Theorem 5-4 • An equilateral triangle is also equiangular • Theorem 5-6 • An equiangular triangle is also equilateral

  6. Theorems (con’t) • Theorem 5-5 • Each of the three lines of symmetry for an equilateral triangle bisects an angle of the triangle and is the perpendicular bisector of the side opposite that angle.

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