Triangles

A triangle is a polygon with three sides.

Classifying Triangles For example, We name a triangle using its vertices. ∆ABC ∆BAC ∆CAB∆CBA ∆BCA ∆ACB

Opposite Sides and Angles We say that is opposite. What is opposite ? What is opposite of ?

Triangles can be classified by their Sides Scalene Isosceles Equilateral Angles Acute Right Obtuse Equiangular

Equilateral Triangle A triangle in which all 3 sides are equal

Isosceles Triangle A triangle in which at least 2 sides are equal

Scalene Triangle A triangle in which all 3 sides are different lengths

Acute Triangle A triangle in which all 3 angles are less than 90˚

Right Triangle A triangle in which exactly one angle is 90˚

Obtuse Triangle A triangle in which exactly one angle is greater than 90˚and less than 180˚

Equiangular Triangle A triangle in which all 3 angles are the same measure.

Angles When the sides of a polygon are extended, other angles are formed. The inside/original angles are the interior angles. The adjacent/outside angles that form linear pairs with the interior angles are the exterior angles. Interior angles Exterior angles <4, <5, <6 <1, <2, <3

TRIANGLE INVESTIGATION

Triangle Sum Theorem The sum of the interior angles in a triangle is 180˚

Find the value of x. Example: x 3x 2x

EXTERIOR TRIANGLE INVESTIGATION

Exterior Angle Theorem The measure of the exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. Exterior Angle Remote Interior Angles A B C D

Find the value of x. Example: x 70 (2x+10)

A corollary to a theorem is a statement that can be proven easily using another theorem. Corollary Definition:

Third Angle Corollary If two angles in one triangle are congruent to two angles in another triangle, then the third angles are congruent.

Equiangular Corollary Each angle in an equiangular triangle is 60˚.

Right Angle Corollary There can be at most one right or obtuse angle in a triangle.

Acute Corollary Acute angles in a right triangle are complementary.