Transcript PPT - FLYPARSONS.org

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
Scalene
(No sides
equal)
Isosceles
(at least two
sides equal)
Equilateral
(all sides
equal)
What’s possible?
Equilateral
Equiangular
Scalene
NO
Acute
Right
NO
Obtuse
Isosceles
NO
Pythagorean Theorem
c2
a2
b2
a2 + b2 = c2
Pythagorean Theorem
http://regentsprep.org/Regents/Math/fpyth/PracPyth.htm
Pythagorean Theorem
http://regentsprep.org/Regents/Math/fpyth/PracPyth.htm
Pythagorean Theorem
http://regentsprep.org/Regents/Math/fpyth/PracPyth.htm
Pythagorean Theorem
http://regentsprep.org/Regents/Math/fpyth/PracPyth.htm
Testing for acute, obtuse, right
2 + b2 = c2
a
Pythagorean theorem says:
What happens if
a2 + b2 > c2
or
a2 + b2 < c2
Testing for acute, obtuse, right
Right triangle: a2 + b2 = c2
Acute triangle: a2 + b2 > c2
Obtuse triangle: a2 + b2 < c2
Types of Angles
Website
www.mrperezonlinemathtutor.com
 Complementary
 Supplementary
 Adjacent
 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
Trapezoid
Parallelogram
Rhombus
Rectangle
Square
Kite
Are diagonals
perpendicular?
For which shapes will the diagonals
always be perpendicular?
Type of
Quadrilateral
Are diagonals
perpendicular?
Trapezoid
maybe
Parallelogram
Rhombus
Rectangle
Square
Kite
For which shapes will the diagonals
always be perpendicular?
Type of
Quadrilateral
Are diagonals
perpendicular?
Trapezoid
maybe
Parallelogram
maybe
Rhombus
Rectangle
Square
Kite
For which shapes will the diagonals
always be perpendicular?
Type of
Quadrilateral
Are diagonals
perpendicular?
Trapezoid
maybe
Parallelogram
maybe
Rhombus
yes
Rectangle
Square
Kite
For which shapes will the diagonals
always be perpendicular?
Type of
Quadrilateral
Are diagonals
perpendicular?
Trapezoid
maybe
Parallelogram
maybe
Rhombus
yes
Rectangle
maybe
Square
Kite
For which shapes will the diagonals
always be perpendicular?
Type of
Quadrilateral
Are diagonals
perpendicular?
Trapezoid
maybe
Parallelogram
maybe
Rhombus
yes
Rectangle
maybe
Square
yes
Kite
For which shapes will the diagonals
always be perpendicular?
Type of
Quadrilateral
Are diagonals
perpendicular?
Trapezoid
maybe
Parallelogram
maybe
Rhombus
yes
Rectangle
maybe
Square
yes
Kite
yes
Area Formulas: Triangle
http://illuminations.nctm.org/LessonDetail.aspx?ID=L577
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
Area Formulas: Triangle