Download Triangle Properties and Classification

Recall that a triangle ( ) is a polygon with three
sides. Triangles can be classified in two ways: by
their angle measures or by their side lengths.
C
A
B
AB, BC, and AC are the sides of ABC.
A, B, C are the triangle's vertices.
Triangle Classification By Angle Measures
Acute Triangle
Three acute angles
Triangle Classification By Angle Measures
Equiangular Triangle
Three congruent acute angles
Triangle Classification By Angle Measures
Right Triangle
One right angle
Triangle Classification By Angle Measures
Obtuse Triangle
One obtuse angle
Triangle Classification By Side Lengths
Equilateral Triangle
Three congruent sides
Triangle Classification By Side Lengths
Isosceles Triangle
At least two congruent sides
Triangle Classification By Side Lengths
Scalene Triangle
No congruent sides
Remember!
When you look at a figure, you cannot assume segments are congruent based on
appearance. They must be marked as congruent.
Warm Up
1. Find each angle measure.
60°; 60°; 60°
True or False. If false explain.
2. Every equilateral triangle is isosceles.
True
3. Every isosceles triangle is equilateral.
False; an isosceles triangle can have only two
congruent sides.
Recall that an isosceles triangle has at least two congruent sides. The congruent sides
are called the legs. The vertex angle is the angle formed by the legs. The side opposite
the vertex angle is called the base, and the base angles are the two angles that have
the base as a side.
3 is the vertex angle.
1 and 2 are the base angles.
The following corollary and its converse show the connection between equilateral
triangles and equiangular triangles.
The interior is the set of all points inside the figure. The exterior is the set of all
points outside the figure.
Exterior
Interior
An interior angle is formed by two sides of a triangle. An exterior angle is formed
by one side of the triangle and extension of an adjacent side.
4 is an exterior angle.
Exterior
Interior
3 is an interior angle.
A corollary is a theorem whose proof follows directly from another theorem. Here
are two corollaries to the Triangle Sum Theorem.
Triangles are congruent if they are the same size and shape and all
Corresponding angles and all corresponding sides are congruent.
Helpful Hint
When you write a statement such as ABC 
DEF, you are also stating which parts are
congruent.
Example 1: Naming Congruent Corresponding Parts
Given: ∆PQR  ∆STW
Identify all pairs of corresponding congruent parts.
Angles: P  S, Q  T, R  W
Sides: PQ  ST, QR  TW, PR  SW