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Mastering Isosceles & Equilateral Triangles: Key Theorems & Angle Calculations

Learn about the parts of an isosceles triangle, base angles theorem, angle calculations, and perimeter calculations. Practice finding missing angles and variables using given theorems and angles. Enhance your geometry skills!

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Mastering Isosceles & Equilateral Triangles: Key Theorems & Angle Calculations

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  1. Unit 4 Lesson 6 NotesUse Isosceles and Equilateral Triangles

  2. Parts of an Isosceles Triangle leg leg base Angles opposite the congruent sides Angle between the congruent sides Side not congruent Sides congruent

  3. Base Angles Theorem: • If two sides of a triangle are ___________, then • the ________ ____________ the sides are • ____________. congruent angles opposite congruent

  4. Theorem (converse of the Base Angles Theorem): • If two angles of a triangle are congruent, then the sidesopposite the angles are congruent.

  5. 40° 6 6 a b 1. Find the missing angles. 70° 180 – 40 2 a = = 70° b = 70°

  6. 1. Find the missing angles. 30° a = 120° 180 – 30 – 30 = b = 30°

  7. 1. Find the missing angles. 180 3 = 60° 60° 60° 60°

  8. 1. Find the missing angles. 90 2 = 45° a 45° 45° b

  9. 2. Find the missing variables. 45° 45° y + 7 = 45 3x = 45 x = 15 y = 38

  10. 2. Find the missing variables. 3x – 11 = 2x + 11 x – 11 = 11 x = 22° 55° 55° 55° 3(22) – 11 = 2y + 55 + 55 = 180 2y + 110 = 180 2y = 70 y = 35°

  11. 2. Find the missing variables. 32° 32° 58° 58°

  12. 2. Find the missing variables. 65° 25° 130° 50° 25° 65°

  13. 3. Find the perimeter of the triangle. 2x – 1 = x + 4 9ft x – 1 = 4 9ft x = 5 P = 9 + 9 + 7 P = 25ft

  14. 3. Find the perimeter of the triangle. 10x – 32 = 5x – 7 18in 5x – 32 = –7 5x = 25 x = 5 P = 18+18+14 P = 50in 18in

  15. 3. Find the perimeter of the triangle. 3x – 1 = x + 13 20ft 20ft 2x – 1 = 13 2x = 14 x = 7 20ft P = 20+20+20 P = 60ft

  16. HW Problem # 16 x + 7 = 55 55 x = 48° y + 55 + 55 = 180 y + 110 = 180 y = 70°

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