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