Classifying triangles

Sec 4.1Sol:

How many ways can you classify a triangle?

Angle sums in a triangle

The sum of the measures of the interior angles and exterior angles of a triangle are 180°.

Hands on activity

Polygon – is a closed figure in a plane that is made up of segments, called sides that intersect only at their endpoints, called vertices.

Triangle – is a three sided polygon. You name them by their vertices.

A

C B

Parts of a triangleSides

Vertices

Angles

Opposite Sides

The opposite side is the side that is across from the angle, it is the side that has nothing to do with forming the angle.

The side opposite A is _____The side opposite B is _____The side opposite C is _____

A

C B

Classifying Triangles

There are two ways to Classify Triangles.1. By their Angles

a. Acuteb. Equiangularc. Obtused. Right

2. By the number of Congruent Sides they have.a. Scaleneb. Isoscelesc. Equilateral

Acute triangle:

All the angles are Acute (All the angles measures are < (less than) 90°.

A

C B

Mrs. Acute

Equiangular Triangle

is a special type of Acute triangle.All Angles are congruent.Each angle has a measure of 60°.

A

C B

Mrs. Equiangular

Obtuse Triangles

Has only one angle that is obtuse. This angle has a measure > (greater than) 90°

but < (less than) 180°.

A

C B

Mr. Obtuse

Right Triangles

Has only one angle that is a right angle.Meaning only one angle has a measure of 90°.

The sides of a right triangle have special names:a) The side opposite the right angle is the________________b) The two sides that form the right angles are the_________

Mrs. RightA

C B

Hypotenuse

Legs

Use the triangle below, identify the following:

Sides Vertices Angles Hypotenuse Legs

A

C B

Scalene Triangle

No two side are Congruent. Meaning all the side have different side

lengths.

A

C

B

Mr. Scalene

Isosceles Triangles

At least two side are congruent.

Mrs. Isosceles

BA = 3.36 cm

CA = 3.36 cm A

C

B

Like a right Triangle the parts of an Isosceles triangle have special names.

leg leg

The angle formed by the congruent sides is called the

VERTEX ANGLE

The side opposite the vertex the called the BASE

The congruent sides are called LEGS

The two angles formed by the base and one of the

congruent sides are called BASE ANGLES.

Equilateral Triangles

All the sides are congruent. Is a special type of Acute triangle. Is also considered to be Isosceles.

A

B

C

Mr. Equilateral

ExamplesTriangle PQR is an equilateral triangle. One side measures 2x + 5 and

another side measures x + 35. Find the length of each side.

x + 35

2x + 5

Q

R

P

ST = ______________

TU = ______________

SU = ______________

Given STU, with vertices S(2, 3), T(4, 3) and U(3, – 2) , use the distance formula to prove

STU is isosceles.

Assignments

Classwork: Handout

Homework: Handout