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

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

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

What’s possible? EquilateralIsoscelesScalene Equiangular Acute Right Obtuse NO

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

Pythagorean Theorem

Pythagorean Theorem

Pythagorean Theorem

Pythagorean Theorem

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

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

Types of Angles Website  Complementary Complementary  Supplementary Supplementary  Adjacent Adjacent  Vertical Vertical

Transversals

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

Angles in pattern blocks

Diagonals Joining two nonadjacent vertices of a polygon

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

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

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

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

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

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

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

Area Formulas: Triangle 

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?

Area Formulas: Triangle