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Isosceles and Equilateral Triangles

Isosceles and Equilateral Triangles. Geometry (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 and Vertex angle—angle formed by the legs < A

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Isosceles and Equilateral Triangles

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  1. Isosceles and Equilateral Triangles Geometry (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 and Vertex angle—angle formed by the legs < A Base—side opposite the vertex angle Base angles—two angles that have the base as a side < B and < C

  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 m< B = m< A = x m < C + m < B + m < A = 180 x+ 50 + 50 = 180 x + 100 = 180 x = 80 which means m< C = 80

  6. Example—finding angle measures A Find the measure of < C. 50 x C B m< C = m< B = x m < C + m < B + m < A = 180 x + x + 50 = 180 2x + 50 = 180 2x = 130 x = 65 which means m < C = 65

  7. Example—finding angle measures (algebraic) S Find x. x + 38 T 3x R m < R = m < S 3x = x + 38 2x = 38 x = 19

  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 triangle is equilateral-----equiangular each angle is 60 4x + 12 = 60 4x = 48 x = 12

  11. Example—finding sides J Find t. 3t + 3 K 5t – 9 L Triangle is equiangular---equilateral (all equal sides) 5t – 9 = 3t + 3 2t – 9 = 3 2t = 12 t = 6

  12. Example—Multiple Triangles Find the measures of the numbered angles. 80 5 m< 3 = m< 4 x + x + 80 = 180 2x + 80 = 180 2x = 100 3 4 1 2 x = 50 so m <3 and m < 4 = 50 m< 1 and m< 4 are supplementary m< 1 + m < 4 = 180 m< 1 + 50 = 180 m< 1 = 130 m< 1 + m< 2 + m< 5 = 180 with m< 2 = m< 5 130 + y + y = 180 130 + 2y = 180 2y = 50 y = 25 so m< 2 = 25, and m< 5 = 25

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