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) C A B adjacent Side opposite A

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

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

Example 1: 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.

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

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

Example 2b: Identify the scalene triangles in the figure if Scalene triangles have no congruent sides. Answer: VYX, ZTX, VZU, YTU, VWX, ZUX, and YXU are scalene.

Example 2c: Identify the indicated triangles in the figure. a. isosceles triangles Answer: ADE, ABE b. scalene triangles Answer: ABC, EBC, DEB, DCE, ADC, ABD

Example 3: 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 3: Next, substitute to find the length of each side. KL = 7 LM = 7 KM = 7 Answer: For KLM, and the measure of each side is 7.

Your Turn: ALGEBRA Find x and the measure of each side of equilateral triangle if and Answer:

Example 4: COORDINATE GEOMETRY Find the measures of the sides of RST. Classify the triangle by sides.

Example 4: Use the distance formula to find the lengths of each side. Answer: ; since all 3 sides have different lengths, RST is scalene.

Assignment Pre-AP Geometry: Pg. 181 #13 – 18, 22 – 29, 32, 34, 36, 38