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Isosceles and Equilateral Triangles

Isosceles and Equilateral Triangles. Section 5-1. Isosceles Triangle. A triangle with at least two congruent sides. Vertex Angle. Leg. Leg. Base Angles. Base. Equilateral Triangle. A triangle with all equal sides. Theorems. Theorem 5-1 (Isosceles Triangle Theorem)

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Isosceles and Equilateral Triangles

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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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