Classifying triangles

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Presentation transcript:

Classifying triangles Sec 4.1 Sol: How many was 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. Parts of a triangle Sides 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 _____

Classifying Triangles There are two ways to Classify Triangles. 1. By their Angles a. Acute b. Equiangular c. Obtuse d. Right 2. By the number of Congruent Sides they have. a. Scalene b. Isosceles c. Equilateral

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

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

Obtuse Triangles Has only one angle that is obtuse. This angles has a measure > (greater than) 90° but < (less than) 180°. 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. Right Hypotenuse Legs

Use the triangle below, identify the following: Sides Vertices Angles Hypotenuse Legs

Scalene Triangle No two side are Congruent. Meaning all the side have different side lengths. Mr. Scalene

Isosceles Triangles At least two side are congruent. Mr. Isosceles

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

Examples Triangle PQR is an equilateral triangle. One side measures 2x + 5 and another side measures x + 35. Find the length of each side.

Given STU, with vertices S(2, 3), T(4, 3) and U(3, – 2) , use the distance formula to prove STU is isosceles. ST = ______________ TU = ______________ SU = ______________

Assignments Classwork: Workbook Pg: 41 and 42 1-9 Homework: Pg 181-182 22-36