1. Triangle Discoveries Work with a part to see what discoveries can you make about triangles.

2. Types of Triangles Classified by Angles  Equiangular: all angles congruent  Acute: all angles acute  Obtuse: one obtuse angle  Right: one right angle Classified by Sides  Equilateral: all sides congruent  Isosceles: at least two sides congruent  Scalene: no sides congruent

3. Triangles Isosceles (at least two sides equal) Scalene (No sides equal) Equilateral (all sides equal)

4. What’s possible? EquilateralIsoscelesScalene Equiangular Acute Right Obtuse NO

5. Pythagorean Theorem a2a2 b2b2 c2c2 a 2 + b 2 = c 2

6. Pythagorean Theorem http://regentsprep.org/Regents/Math/fpyth/PracPyth.htm

7. Pythagorean Theorem http://regentsprep.org/Regents/Math/fpyth/PracPyth.htm

8. Pythagorean Theorem http://regentsprep.org/Regents/Math/fpyth/PracPyth.htm

9. Pythagorean Theorem http://regentsprep.org/Regents/Math/fpyth/PracPyth.htm

10. Testing for acute, obtuse, right Pythagorean theorem says: What happens if or a 2 + b 2 = c 2 a 2 + b 2 > c 2 a 2 + b 2 < c 2

11. Testing for acute, obtuse, right Right triangle: Acute triangle: Obtuse triangle: a 2 + b 2 = c 2 a 2 + b 2 > c 2 a 2 + b 2 < c 2

12. Types of Angles Website www.mrperezonlinemathtutor.com  Complementary Complementary  Supplementary Supplementary  Adjacent Adjacent  Vertical Vertical

13. Transversals

14. What is the value of x? 2x + 5 3x + 10

15. Angles in pattern blocks

16. Diagonals Joining two nonadjacent vertices of a polygon

17. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoid Parallelogram Rhombus Rectangle Square Kite

18. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoidmaybe Parallelogram Rhombus Rectangle Square Kite

19. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoidmaybe Parallelogrammaybe Rhombus Rectangle Square Kite

20. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoidmaybe Parallelogrammaybe Rhombusyes Rectangle Square Kite

21. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoidmaybe Parallelogrammaybe Rhombusyes Rectanglemaybe Square Kite

22. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoidmaybe Parallelogrammaybe Rhombusyes Rectanglemaybe Squareyes Kite

23. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoidmaybe Parallelogrammaybe Rhombusyes Rectanglemaybe Squareyes Kiteyes

24. Area Formulas: Triangle  http://illuminations.nctm.org/LessonDetail.aspx?ID=L577 http://illuminations.nctm.org/LessonDetail.aspx?ID=L577

25. Area Formulas: Triangle 1. Using a ruler, draw a diagonal (from one corner to the opposite corner) on shapes A, B, and C. 2. Along the top edge of shape D, mark a point that is not a vertex. Using a ruler, draw a line from each bottom corner to the point you marked. (Three triangles should be formed.) 3. Cut out the shapes. Then, divide A, B, and C into two parts by cutting along the diagonal, and divide D into three parts by cutting along the lines you drew. 4. How do the areas of the resulting shapes compare to the area of the original shape?

26. Area Formulas: Triangle