Download Basic Theorems of Triangles

Basic Theorems of Triangles
Sophomore Geometry
By: Shannon Manzella
Interior Angles Theorem
• In a Triangle, the Interior Angles will always
add to be 180°
– The Interior Angles are the inside angles between
adjacent sides of a rectilinear figure.
Example A
• Solve for angle .
Base Angles Theorem
• If the sides of a triangle are congruent ( like in
an Isosceles triangle) then the angles opposite
these sides are congruent.
– Two angles are congruent if they have the value
and size.
Leg A
Base Angle B
Leg B
Base Angle A
Example B
• Solve for angle .
Example C
• Solve for angle .
The Midpoint Theorem
• The segment joining the midpoints of two
sides of a triangle is parallel to the third side
and half as long as the third side.
– The Midpoint of a line segment is the point that is
halfway between the endpoints of the line
segment.
Example D
Example E
Cites
• http://www.toxel.com/wpcontent/uploads/2012/12/meltedcrayon08.jp
g
• http://www.mathwarehouse.com/geometry/t
riangles/
• http://www.basic-mathematics.com/baseangles-theorem.html
• http://www.cliffsnotes.com/math/geometry/p
olygons/the-midpoint-theorem