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Isosceles and Equilateral Triangles

This educational resource provides a comprehensive overview of isosceles and equilateral triangles, examining their properties and key theorems. Learn to identify the legs, base, and angles of isosceles triangles, and explore the Isosceles Triangle Theorem and its converse. Engage with warm-up activities like unscrambling triangle types and reflect on homework problems. The essential concepts include CPCTC, base angles, and the relationship between sides and angles in isosceles and equilateral triangles. Perfect for students seeking to solidify their understanding of triangle properties.

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Isosceles and Equilateral Triangles

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  1. Brett Solberg AHS ‘11-’12 Isosceles and Equilateral Triangles

  2. Warm-up 1) What does CPCTC mean? Explain it in your own words. Unscramble the letters to reveal a type of triangle. 2) seicslose 3) telqariulae 4) giaqunearul Do you want to review any HW problems?

  3. Isosceles Triangles • A triangle where exactly 2 sides are congruent. • Legs – the 2 congruent sides • Vertex Angle – the angle formed by the legs. • Base – Third side of the triangle. • Base Angles – 2 angles adjacent to the base.

  4. Isosceles Triangles • Identify the legs, base, base angles, and vertex of the triangle. • Legs – • Base – • Base Angles – • Vertex –

  5. Isosceles Triangles • Identify the legs, base, base angles, and vertex of the triangle. • Legs – • Base – • Base Angles – • Vertex –

  6. Isosceles Triangles • Identify the legs, base, base angles, and vertex of the triangle. • Legs – • Base – • Base Angles – • Vertex –

  7. Isosceles Triangle Theorem • If two sides of a triangle are congruent, then the angles opposite them are congruent. • If AB ≅ AC, then ∠B ≅ ∠C

  8. Example

  9. Converse of Isosceles Triangle Thm • If two angles of a triangle are congruent, then the sides opposite them are congruent. • If ∠B ≅ ∠C then AB ≅ AC

  10. Example

  11. Example • Solve for y.

  12. Example • Solve for x.

  13. Example • Solver for x.

  14. Vocab • Bisector • Perpendicular Bisector A B

  15. Theorem 4.5 • The bisector of the vertex angle is the perpendicular bisector of the base.

  16. Isosceles Review • Base Angles Theorem • Converse

  17. Transition

  18. #3 - Corollary to the Base Angles Thm • If a triangle is equilateral, then it is equiangular.

  19. Transition

  20. #4 - Corollary to the Converse of the Base Angles Thm • If a triangle is equiangular, than it is equilateral.

  21. Reflection • What is the measure of the angles of any equiangular triangle? • What is the measure of the angles of any equilateral triangle?

  22. What does this symbol represent?

  23. The Triforce

  24. The Triforce How many equilateral triangles are there in the trifoce?

  25. Example • Find the value of x and y.

  26. Example

  27. Review

  28. Review • If 2 sides of a triangle are congruent, than the angles opposite them are congruent. • If two angles are congruent, then the sides opposite them are congruent.

  29. Review • If a triangle is equilateral, then it is equiangular. • If a triangle is equiangular, then it is equilateral. • The angles in any equilateral or equiangular triangle are 60°.

  30. Homework • 4.5 Worksheet and pg 230#1-13

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