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Isosceles and Equilateral Triangles

Isosceles and Equilateral Triangles. Geometry H2 (Holt 4-9) K.Santos. Parts of an Isosceles Triangle. Isosceles triangle—is a triangle with at least two congruent sides A B C Legs—are the congruent sides Vertex angle—angle formed by the legs

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Isosceles and Equilateral Triangles

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  1. Isosceles and Equilateral Triangles Geometry H2 (Holt 4-9) K.Santos

  2. Parts of an Isosceles Triangle Isosceles triangle—is a triangle with at least two congruent sides A B C Legs—are the congruent sides Vertex angle—angle formed by the legs Base—side opposite the vertex angle Base angles—two angles that have the base as a side

  3. Isosceles Triangle Theorem (4-9-1) If two sides of a triangle are congruent, then the angles opposite the sides are congruent. A B C Given: Then: <A <C congruent sides congruent angles

  4. Converse of the Isosceles Triangle Theorem (4-9-2) If two angles of a triangle are congruent, then the sides opposite those angles are congruent. A B C Given: <A <C Then: congruent angles congruent sides

  5. Example—finding angle measures A Find the measure of <C. 50 C B

  6. Example—finding angle measures A Find the measure of < C. 50 x C B

  7. Example—finding angle measures (algebraic) S Find x. x + 38 T 3x R

  8. Corollary(4-9-3)—Equilateral Triangle If a triangle is equilateral, then it is equiangular. M N O Given: Then: <M <N <O 180/3 = 60 equilateral equiangular

  9. Corollary (4-9-4)—Equiangular Triangle If a triangle is equiangular, then it is equilateral. M N O Given:<M <N <O Then: equiangularequilateral

  10. Example—Finding angles Find x. G 4x+12 H I

  11. Example—finding sides J Find t. 3t + 3 K 5t – 9 L

  12. Example—Multiple Triangles Find the measures of the numbered angles. 80 5 3 4 1 2

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