Classifying Triangles & Angles of Triangles

Sections 4-1 & 4-2

A triangle is the figure formed by 3 segments joining 3 noncollinear points. Each of the 3 points is a vertex. The segments are the sides.

A

BC

CABCABSides ,,:

A, B, CVertices points:

Classifying Triangles by Sides

Scalene Triangle – no sides congruent

Isosceles Triangle – At least 2 sides congruent

Equilateral Triangle – All sides congruent

Classifying Triangles by Angles

Right – 1 right angle

Equiangular – all angles congruent

Acute – 3 acute angles

Obtuse – one obtuse angle

500 600

700

1200

400200

600600

600

Parts of an Isosceles Triangle

legleg

base

vertex angle

base angles

Angle Sum Theorem

The sum of the measures of the angles of a triangle is 180.

400400

1000

Third Angle Theorem

If 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent.

Corollariesstatements that can be easily proved using a theorem

Each angle of an equiangular triangle has measure 60.

In a triangle, there an be at most one right angle or obtuse angle.

The acute angles of a right triangle are complementary.

Exterior Angle TheoremThe measure of an exterior angle of a

triangle equals the sum of the measures of the 2 remote interior angles.

750

350

400Exterior

Remote interiorangles

Joke Time

What has wings and solves number problems?

A mothematician

What did one math book say to the other math book?

Don’t bother me! I’ve got my own problems!

What would a math student say to a fat parrot?

Poly-no-mial