Triangle DiscoveriesTriangle Discoveries

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

Types of TrianglesTypes of Triangles

Classified by AnglesClassified by Angles Equiangular: all angles congruentEquiangular: all angles congruent Acute: all angles acuteAcute: all angles acute Obtuse: one obtuse angleObtuse: one obtuse angle Right: one right angleRight: one right angle

Classified by SidesClassified by Sides Equilateral: all sides congruentEquilateral: all sides congruent Isosceles: at least two sides congruentIsosceles: at least two sides congruent Scalene: no sides congruentScalene: no sides congruent

TrianglesTriangles

Isosceles (at least two sides equal)

Scalene

(No sides equal)

Equilateral (all sides equal)

What’s possible?What’s possible?

EquilateralEquilateral IsoscelesIsosceles ScaleneScalene

EquiangularEquiangular

AcuteAcute

RightRight

ObtuseObtuse

NO

NO

NO

Pythagorean TheoremPythagorean Theorem

a2

b2

c2

a2 + b2 = c2

Pythagorean TheoremPythagorean Theorem

http://regentsprep.org/Regents/Math/fpyth/PracPyth.htm

Pythagorean TheoremPythagorean Theorem

http://regentsprep.org/Regents/Math/fpyth/PracPyth.htm

Pythagorean TheoremPythagorean Theorem

http://regentsprep.org/Regents/Math/fpyth/PracPyth.htm

Pythagorean TheoremPythagorean Theorem

http://regentsprep.org/Regents/Math/fpyth/PracPyth.htm

Testing for acute, obtuse, rightTesting for acute, obtuse, right

Pythagorean theorem says: Pythagorean theorem says:

What happens if What happens if

or or

a2 + b2 = c2

a2 + b2 > c2

a2 + b2 < c2

Testing for acute, obtuse, rightTesting for acute, obtuse, right

Right triangle: Right triangle:

Acute triangle:Acute triangle:

Obtuse triangle: Obtuse triangle:

a2 + b2 = c2

a2 + b2 > c2

a2 + b2 < c2

Types of AnglesTypes of Angles

Website Website

www.mrperezonlinemathtutor.comwww.mrperezonlinemathtutor.com Complementary Complementary SupplementarySupplementary AdjacentAdjacent VerticalVertical

TransversalsTransversals

What is the value of x?What is the value of x?

2x + 5

3x + 10

Angles in pattern blocksAngles in pattern blocks

DiagonalsDiagonals

Joining two nonadjacent vertices of a Joining two nonadjacent vertices of a polygonpolygon

For which shapes will the diagonals For which shapes will the diagonals always be perpendicular?always be perpendicular?

Type of Type of QuadrilateralQuadrilateral

Are diagonals Are diagonals perpendicular?perpendicular?

TrapezoidTrapezoid

ParallelogramParallelogram

RhombusRhombus

RectangleRectangle

SquareSquare

KiteKite

For which shapes will the diagonals For which shapes will the diagonals always be perpendicular?always be perpendicular?

Type of Type of QuadrilateralQuadrilateral

Are diagonals Are diagonals perpendicular?perpendicular?

TrapezoidTrapezoid maybemaybe

ParallelogramParallelogram

RhombusRhombus

RectangleRectangle

SquareSquare

KiteKite

For which shapes will the diagonals For which shapes will the diagonals always be perpendicular?always be perpendicular?

Type of Type of QuadrilateralQuadrilateral

Are diagonals Are diagonals perpendicular?perpendicular?

TrapezoidTrapezoid maybemaybe

ParallelogramParallelogram maybemaybe

RhombusRhombus

RectangleRectangle

SquareSquare

KiteKite

For which shapes will the diagonals For which shapes will the diagonals always be perpendicular?always be perpendicular?

Type of Type of QuadrilateralQuadrilateral

Are diagonals Are diagonals perpendicular?perpendicular?

TrapezoidTrapezoid maybemaybe

ParallelogramParallelogram maybemaybe

RhombusRhombus yesyes

RectangleRectangle

SquareSquare

KiteKite

For which shapes will the diagonals For which shapes will the diagonals always be perpendicular?always be perpendicular?

Type of Type of QuadrilateralQuadrilateral

Are diagonals Are diagonals perpendicular?perpendicular?

TrapezoidTrapezoid maybemaybe

ParallelogramParallelogram maybemaybe

RhombusRhombus yesyes

RectangleRectangle maybemaybe

SquareSquare

KiteKite

For which shapes will the diagonals For which shapes will the diagonals always be perpendicular?always be perpendicular?

Type of Type of QuadrilateralQuadrilateral

Are diagonals Are diagonals perpendicular?perpendicular?

TrapezoidTrapezoid maybemaybe

ParallelogramParallelogram maybemaybe

RhombusRhombus yesyes

RectangleRectangle maybemaybe

SquareSquare yesyes

KiteKite

For which shapes will the diagonals For which shapes will the diagonals always be perpendicular?always be perpendicular?

Type of Type of QuadrilateralQuadrilateral

Are diagonals Are diagonals perpendicular?perpendicular?

TrapezoidTrapezoid maybemaybe

ParallelogramParallelogram maybemaybe

RhombusRhombus yesyes

RectangleRectangle maybemaybe

SquareSquare yesyes

KiteKite yesyes

Area Formulas: TriangleArea Formulas: Triangle

http://illuminations.nctm.org/LessonDetail.aspx?ID=L577http://illuminations.nctm.org/LessonDetail.aspx?ID=L577

Area Formulas: TriangleArea Formulas: Triangle1. Using a ruler, draw a 1. Using a ruler, draw a

diagonal (from one corner diagonal (from one corner to the opposite corner) on to the opposite corner) on shapes A, B, and C.shapes A, B, and C.

2. Along the top edge of shape 2. Along the top edge of shape D, mark a point that is not D, mark a point that is not a vertex. Using a ruler, a vertex. Using a ruler, draw a line from each draw a line from each bottom corner to the point bottom corner to the point you marked. (Three you marked. (Three triangles should be triangles should be formed.)formed.)

3. Cut out the shapes. Then, 3. Cut out the shapes. Then, divide A, B, and C into two divide A, B, and C into two parts by cutting along the parts by cutting along the diagonal, and divide D into diagonal, and divide D into three parts by cutting three parts by cutting along the lines you drew.along the lines you drew.

4. How do the areas of the 4. How do the areas of the resulting shapes compare resulting shapes compare to the area of the original to the area of the original shape?shape?

Area Formulas: TriangleArea Formulas: Triangle

Area Formulas: TriangleArea Formulas: Triangle