Sides of a Triangle (Lengths)
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Transcript of Sides of a Triangle (Lengths)
Sides of a Triangle(Lengths)
1
The addition of the lengths of any two sides of a triangle must be greater than the third.
a b
ca + b >c a+ c> b c + b>a
1
Angles of a Triangle
2
Sum to 180˚
B
A C
m<A + m< B +m< C = 180˚
2
Exterior angle of a Triangle
3
The sum of the two non-adjacent angles of the triangle is equal to the measure of the exterior angle.
B
A C D
m<A + m<B = m<BCD
3
Special Right Triangle(30˚, 60˚, 90˚)
4
Side opposite 30˚= ½ hypotenuseSide opposite 60˚= ½ hypotenuse
60
Hypotenuse Side opp 30
30
Side opp 60
4
3
Special Right Triangle(45˚, 45˚, 90˚)
5
Hypotenuse = leg 45
Hyp Leg
45
Leg
5
2
Similar Triangles~
6
• corresponding angles are congruent• corresponding sides are in proportion.
6
Isosceles Triangle
7
A triangle that contains two congruent sides and angles
7
Isosceles Right Triangle
8
45
Hyp Leg
45
Leg
8
(45˚, 45˚, 90˚)
Median of a triangle
9
A line that is drawn form the vertex of a triangle to the midpoint
of the opposite side
9
Altitude of a Triangle
10
The altitude of a triangle is a line segment extending from any vertex of
a triangle perpendicular to the line containing the opposite side.
10
Altitude