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4.1 Triangles and Angles. Definition: Triangle. A triangle is a figure formed by three segments joining three noncollinear points . Triangles are always classified in two ways: By Sides By Angles. Subtending Angles & Sides. - PowerPoint PPT Presentation
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4.1 Triangles and Angles
Definition: Triangle
A triangle is a figure formed by three segments joining three noncollinear points.
Triangles are always classified in two ways:1. By Sides2. By Angles
Subtending Angles & Sides• When two sides are equal then their subtending angles
must be equal. • Likewise, when two angles are equal then their
subtending sides must be equal.Angle A subtends Side BCAngle B subtends Side ACAngle C subtends Side AB
If AB = BC, then which two angles must be equal?
If <B = <C, then which two sides must be equal?
A
B
C
Classification by SidesEquilateral Triangle = 3 congruent sides
Isosceles Triangle = At least 2 congruent sides
Scalene Triangle = No congruent sides
Classification by AnglesAcute Triangle: Three Acute Angles (all measure less than 90o)
Equiangular Triangle: Three congruent angles (each measures 60o)
Right Triangle; One Right Angle (90o)
Obtuse Triangle: One obtuse Angle (more than 90o) and two acute angles (less than 90o)
Example 1: Classifying Triangles
When you classify a triangle, you must give TWO classifications (sides & angles.)
How would you classify triangle ABC?
Sides: _____________
Angles: ____________
Example 2: Classifying Triangles
How would you classify this triangle?
Sides: _____________
Angles: ____________
Example 3: Classifying Triangles
How would you classify this triangle?
Sides:
Angles:
Special Labels for Right and Isosceles Triangles
Hypotenuse
Leg
LegBase
Leg Leg
By extending the sides we create Interior and Exterior Angles
Interior Angles are “inside” the triangle. Exterior Angles are “outside the triangle. Label each interior angle with an “I” and each exterior angle with an “E.” When an interior angle and an exterior angle are together they make a straight line and sum to 180o.
Triangle Sum Theorem
• The three angles inside of a triangle must always add to 180o.
180m A m B m C
If m<A = 75o and m<B = 85o, what must the measure of angle C be?
A special and useful property!• The measure of an exterior angle of a triangle is equal to
the sum of the measures of the 2 nonadjacent interior angles
1A
B
C
1m m A m B If m<A = 90o and m<B = 45o, then what is m<1?
If m<1 = 102o and m<B = 55o, then what is m<A?
