4.1 Classifying Triangles

Objectives  Identify and classify triangles by angles  Identify and classify triangles by sides

Parts of a Triangle  A triangle is a 3-sided polygon  The sides of ∆ABC are AB, BC, and AC  The vertices of ∆ABC are A, B, and C  Two sides sharing a common vertex are adjacent sides  The third side is called the opposite side  All sides can be adjacent or opposite (it just depends which vertex is being used) adjacent Side opposite  A C A B

Classifying Triangles by Angles Obtuse Obtuse 1 angle is obtuse (measure > 90°) Right 1 angle is right (measure = 90°) One way to classify triangles is by their angles… Acute Acute all 3 angles are acute (measure < 90°) An acute ∆ with all angles  is an equiangular ∆.

ARCHITECTURE The triangular truss below is modeled for steel construction. Classify  JMN,  JKO, and  OLN as acute, equiangular, obtuse, or right. Example 1: 60°

Answer:  JMN has one angle with measure greater than 90, so it is an obtuse triangle.  JKO has one angle with measure equal to 90, so it is a right triangle.  OLN is an acute triangle with all angles congruent, so it is an equiangular triangle. Example 1 cont:

Classifying Triangles by Sides Isosceles Isosceles 2 congruent sides Scalene Scalene no congruent sides Another way to classify triangles is by their sides… Equilateral Equilateral 3 congruent sides

Answer:  UTX and  UVX are isosceles. Identify the isosceles triangles in the figure if Isosceles triangles have at least two sides congruent. Example 2:

Identify the scalene triangles in the figure if Answer:  VYX,  ZTX,  VZU,  YTU,  VWX,  ZUX, and  YXU are scalene. Scalene triangles have no congruent sides. Example 3:

Identify the indicated triangles in the figure. a. isosceles triangles b. scalene triangles Answer:  ABC,  EBC,  DEB,  DCE,  ADC,  ABD Answer:  ADE,  ABE Example 4:

ALGEBRA Find d and the measure of each side of equilateral triangle KLM if and Since  KLM is equilateral, each side has the same length. So 5 = d Example 5:

Next, substitute to find the length of each side. Answer: For  KLM, and the measure of each side is 7. Example 5 cont: KL = 7 LM = 7KM = 7

Answer: ALGEBRA Find x and the measure of each side of equilateral triangle if and Example 6:

COORDINATE GEOMETRY Find the measures of the sides of  RST. Classify the triangle by sides. Example 7:

Answer: ; since all 3 sides have different lengths,  RST is scalene. Use the distance formula to find the lengths of each side. Example 7 cont:

Assignment  Geometry: Pg. 180 #5 - 10, 13-18,